Institute of Scientific and Technical Information of China (English)
吴宁; 阮图南
1996-01-01
A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.
A quantum mechanical model of "dark matter"
Belokurov, V V
2014-01-01
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
A Process Model of Quantum Mechanics
Sulis, William
2014-01-01
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has th...
Molecular model with quantum mechanical bonding information.
Bohórquez, Hugo J; Boyd, Russell J; Matta, Chérif F
2011-11-17
The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.
Mathematical model I. Electron and quantum mechanics
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical model I. Electron and quantum mechanics
Directory of Open Access Journals (Sweden)
Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Quantum Mechanics/Molecular Mechanics Modeling of Drug Metabolism
DEFF Research Database (Denmark)
Lonsdale, Richard; Fort, Rachel M; Rydberg, Patrik;
2016-01-01
The mechanism of cytochrome P450(CYP)-catalyzed hydroxylation of primary amines is currently unclear and is relevant to drug metabolism; previous small model calculations have suggested two possible mechanisms: direct N-oxidation and H-abstraction/rebound. We have modeled the N-hydroxylation of (R......)-mexiletine in CYP1A2 with hybrid quantum mechanics/molecular mechanics (QM/MM) methods, providing a more detailed and realistic model. Multiple reaction barriers have been calculated at the QM(B3LYP-D)/MM(CHARMM27) level for the direct N-oxidation and H-abstraction/rebound mechanisms. Our calculated barriers...... indicate that the direct N-oxidation mechanism is preferred and proceeds via the doublet spin state of Compound I. Molecular dynamics simulations indicate that the presence of an ordered water molecule in the active site assists in the binding of mexiletine in the active site...
Hidden variable models for quantum mechanics can have local parts
Larsson, Jan-Ake
2009-01-01
We present an explicit nonlocal nonsignaling model which has a nontrivial local part and is compatible with quantum mechanics. This model constitutes a counterexample to Colbeck and Renner's statement [Phys. Rev. Lett. 101, 050403 (2008)] that "any hidden variable model can only be compatible with quantum mechanics if its local part is trivial". Furthermore, we examine Colbeck and Renner's definition of "local part" and find that, in the case of models reproducing the quantum predictions for the singlet state, it is a restriction equivalent to the conjunction of nonsignaling and trivial local part.
Models on the boundary between classical and quantum mechanics.
Hooft, Gerard 't
2015-08-06
Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.
Are quantum-mechanical-like models possible, or necessary, outside quantum physics?
Plotnitsky, Arkady
2014-12-01
This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
A simplified quantum mechanical model of diatomic molecules
DEFF Research Database (Denmark)
Nielsen, Lars Drud
1978-01-01
A one-dimensional molecule model with Coulomb potentials replaced by delta functions is introduced. The mathematical simplicity of the model facilitates the quantum mechanical treatment and offers a straightforward demonstration of the essentials of two-particle problems. In spite of the crudeness...
Rae, Alastair I M
2016-01-01
A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...
Solvable time-dependent models in quantum mechanics
Cordero-Soto, Ricardo J.
In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrodinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrodinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrodinger equation in Rn with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrodinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models
Powell, John L
2015-01-01
Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ
Quantum gauge models without (classical) Higgs mechanism
Energy Technology Data Exchange (ETDEWEB)
Duetsch, Michael [Univ. Goettingen, Courant Research Center ' ' Higher order Structures in Mathematics' ' , Mathematisches Institut, Goettingen (Germany); Gracia-Bondia, Jose M. [Universidad de Zaragoza, Departamento de Fisica Teorica, Zaragoza (Spain); Scheck, Florian [Johannes Gutenberg-Universitaet, Institut fuer Physik, Theoretische Elementarteilchenphysik, Mainz (Germany); Varilly, Joseph C. [Universidad de Costa Rica, Escuela de Matematica, San Jose (Costa Rica)
2010-10-15
We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories. (orig.)
Quantum Structures of Model-Universe: Questioning the Everett Interpretation of Quantum Mechanics
Jeknic-Dugic, J; Francom, A
2011-01-01
Our objective is to demonstrate an inconsistency with both the original and modern Everettian Many Worlds Interpretations. We do this by examining two important corollaries of the universally valid quantum mechanics in the context of the Quantum Brownian Motion (QBM) model: "Entanglement Relativity" and the "parallel occurrence of decoherence." We conclude that the highlighted inconsistency demands that either there is a privileged spatial structure of the QBM model universe or that the Everettian Worlds are not physically real.
Quark Model in the Quantum Mechanics Curriculum.
Hussar, P. E.; And Others
1980-01-01
This article discusses in detail the totally symmetric three-quark karyonic wave functions. The two-body mesonic states are also discussed. A brief review of the experimental efforts to identify the quark model multiplets is given. (Author/SK)
Quark Model in the Quantum Mechanics Curriculum.
Hussar, P. E.; And Others
1980-01-01
This article discusses in detail the totally symmetric three-quark karyonic wave functions. The two-body mesonic states are also discussed. A brief review of the experimental efforts to identify the quark model multiplets is given. (Author/SK)
Mandl, F.
1992-07-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.
An Interacting N = 2 Supersymmetric Quantum Mechanical Model: Novel Symmetries
Krishna, S; Malik, R P
2015-01-01
We demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting N = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realization of the de Rham cohomological operators of differential geometry. We derive the nilpotent N = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our N = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables, obtained after the imposition of the SUSY invariant restrictions, and...
Dimer Models, Free Fermions and Super Quantum Mechanics
Dijkgraaf, R; Reffert, S
2007-01-01
This note relates topics in statistical mechanics, graph theory and combinatorics, lattice quantum field theory, super quantum mechanics and string theory. We give a precise relation between the dimer model on a graph embedded on a torus and the massless free Majorana fermion living on the same lattice. A loop expansion of the fermion determinant is performed, where the loops turn out to be compositions of two perfect matchings. These loop states are sorted into co-chain groups using categorification techniques similar to the ones used for categorifying knot polynomials. The Euler characteristic of the resulting co-chain complex recovers the Newton polynomial of the dimer model. We re-interpret this system as supersymmetric quantum mechanics, where configurations with vanishing net winding number form the ground states. Finally, we make use of the quiver gauge theory - dimer model correspondence to obtain an interpretation of the loops in terms of the physics of D-branes probing a toric Calabi-Yau singularity...
Fitzpatrick, Richard
2015-01-01
Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-dependent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.
Ghosh, P K
2014-01-01
Quantum mechanics, designed for advanced undergraduate and graduate students of physics, mathematics and chemistry, provides a concise yet self-contained introduction to the formal framework of quantum mechanics, its application to physical problems and the interpretation of the theory. Starting with a review of some of the necessary mathematics, the basic concepts are carefully developed in the text. After building a general formalism, detailed treatment of the standard material - the harmonic oscillator, the hydrogen atom, angular momentum theory, symmetry transformations, approximation methods, identical particle and many-particle systems, and scattering theory - is presented. The concluding chapter discusses the interpretation of quantum mechanics. Some of the important topics discussed in the book are the rigged Hilbert space, deformation quantization, path integrals, coherent states, geometric phases, decoherene, etc. This book is characterized by clarity and coherence of presentation.
Ahn, Doyeol
2011-01-01
A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...
Operational dynamic modeling transcending quantum and classical mechanics.
Bondar, Denys I; Cabrera, Renan; Lompay, Robert R; Ivanov, Misha Yu; Rabitz, Herschel A
2012-11-09
We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.
Rae, Alastair I M
2007-01-01
PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC
Zagoskin, Alexandre
2015-01-01
Written by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, ra
Quantum mechanical effects analysis of nanostructured solar cell models
Directory of Open Access Journals (Sweden)
Badea Andrei
2016-01-01
Full Text Available The quantum mechanical effects resulted from the inclusion of nanostructures, represented by quantum wells and quantum dots, in the i-layer of an intermediate band solar cell will be analyzed. We will discuss the role of these specific nanostructures in the increasing of the solar cells efficiency. InAs quantum wells being placed in the i-layer of a gallium arsenide (GaAs p-i-n cell, we will analyze the quantum confined regions and determine the properties of the eigenstates located therein. Also, we simulate the electroluminescence that occurs due to the nanostructured regions.
N= 4 Supersymmetric Quantum Mechanical Model: Novel Symmetries
Krishna, S
2016-01-01
We discuss a set of novel discrete symmetry transformations of the N = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent N = 4 SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions onto (1, 4)-dimensional supermanifold.
Sachdev-Ye-Kitaev model as Liouville quantum mechanics
Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
2016-10-01
We show that the proper inclusion of soft reparameterization modes in the Sachdev-Ye-Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ - 3 / 2 for times larger than the inverse single particle level spacing τ ≫ Nln N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ɛ 1 / 2. We also present exact diagonalization study supporting our conclusions.
𝒩 = 4 supersymmetric quantum mechanical model: Novel symmetries
Krishna, S.
2017-04-01
We discuss a set of novel discrete symmetry transformations of the 𝒩 = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent 𝒩 = 4 SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions 𝜃α and 𝜃¯α onto (1, 4)-dimensional supermanifold.
Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
Bagrets, Dmitry; Kamenev, Alex
2016-01-01
We show that the proper inclusion of soft reparameterization modes in the Sachdev-Ye-Kitaev model of $N$ randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent $\\propto \\tau^{-3/2}$ for times larger than the inverse single particle level spacing $\\tau\\gg N\\ln N$. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as $\\epsilon^{1/2}$. We also present exact diagonalization study supporting our conclusions.
Early Atomic Models - From Mechanical to Quantum (1904-1913)
Baily, Charles
2012-01-01
A complete history of early atomic models would fill volumes, but a reasonably coherent tale of the path from mechanical atoms to the quantum can be told by focusing on the relevant work of three great contributors to atomic physics, in the critically important years between 1904 and 1913: J. J. Thomson, Ernest Rutherford and Niels Bohr. We first examine the origins of Thomson's mechanical atomic models, from his ethereal vortex atoms in the early 1880's, to the myriad "corpuscular" atoms he proposed following the discovery of the electron in 1897. Beyond predictions for the periodicity of the elements, the application of Thomson's atoms to problems in scattering and absorption led to quantitative predictions that were confirmed by experiments with high-velocity electrons traversing thin sheets of metal. Still, the much more massive and energetic {\\alpha}-particles being studied by Rutherford were better suited for exploring the interior of the atom, and careful measurements on the angular dependence of their...
Jensen, L; Swart, M; van Duijnen, PT
2005-01-01
A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to mac
Preon models, relativity, quantum mechanics and cosmology (I)
Gonzalez-Mestres, Luis
2009-01-01
Preons are hypothetic constituents of the standard particles. They were initially assumed to have basically similar properties to those of conventional matter. But this is not necessarily the case: the ultimate constituents of matter may feel a different space-time from that of special relativity and exhibit mechanical properties different from those predicted by standard quantum mechanics. They can also play an important cosmological role (inflation, dark matter, dark energy...). It is even not obvious that energy and momentum would have to be conserved in such a scenario. In this series of papers, we review the subject using the superbradyon model as an example, and suggest new ways to explore possible tests of the preon hypothesis.
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Directory of Open Access Journals (Sweden)
Tadashi Okazaki
2015-01-01
Full Text Available We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N=16 and N=12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2 and SU(1,1|6 quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi–Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N=8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Solitons in Skyrme - Faddeev spinor model and quantum mechanics
Rybakov, Y.
2016-07-01
We discuss the possibility of unification of Skyrme and Faddeev approaches for the description of baryons and leptons respectively as topological solitons within the scope of 16-spinor model. The motivation for such a unification is based on a special 8- semispinor identity invented by the Italian geometrician F. Brioschi. This remarkable identity permits one to realize baryon or lepton states through the effect of spontaneous symmetry breaking emerging due to special structure of the Higgs potential in the model. At large distances from the particle - soliton small excitation of the vacuum satisfies Klein - Gordon equation with some mass that permits one to establish the correspondence with quantum mechanics in special stochastic representation of the wave function for extended particles - solitons. Finally, we illustrate the peculiar properties of stochastic representation by the famous T. Young's experiment with n slits in soliton realization.
Mandl, Franz
1992-01-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient
Links between fluid mechanics and quantum mechanics: a model for information in economics?
Haven, Emmanuel
2016-05-28
This paper tallies the links between fluid mechanics and quantum mechanics, and attempts to show whether those links can aid in beginning to build a formal template which is usable in economics models where time is (a)symmetric and memory is absent or present. An objective of this paper is to contemplate whether those formalisms can allow us to model information in economics in a novel way.
The quantum mechanics of cosmology.
Hartle, James B.
The following sections are included: * INTRODUCTION * POST-EVERETT QUANTUM MECHANICS * Probability * Probabilities in general * Probabilities in Quantum Mechanics * Decoherent Histories * Fine and Coarse Grained Histories * Decohering Sets of Coarse Grained Histories * No Moment by Moment Definition of Decoherence * Prediction, Retrodiction, and History * Prediction and Retrodiction * The Reconstruction of History * Branches (Illustrated by a Pure ρ) * Sets of Histories with the Same Probabilities * The Origins of Decoherence in Our Universe * On What Does Decoherence Depend? * Two Slit Model * The Caldeira-Leggett Oscillator Model * The Evolution of Reduced Density Matrices * Towards a Classical Domain * The Branch Dependence of Decoherence * Measurement * The Ideal Measurement Model and the Copenhagen Approximation to Quantum Mechanics * Approximate Probabilities Again * Complex Adaptive Systems * Open Questions * GENERALIZED QUANTUM MECHANICS * General Features * Hamiltonian Quantum Mechanics * Sum-Over-Histories Quantum Mechanics for Theories with a Time * Differences and Equivalences between Hamiltonian and Sum-Over-Histories Quantum Mechanics for Theories with a Time * Classical Physics and the Classical Limit of Quantum Mechanics * Generalizations of Hamiltonian Quantum Mechanics * TIME IN QUANTUM MECHANICS * Observables on Spacetime Regions * The Arrow of Time in Quantum Mechanics * Topology in Time * The Generality of Sum Over Histories Quantum Mechanics * THE QUANTUM MECHANICS OF SPACETIME * The Problem of Time * General Covariance and Time in Hamiltonian Quantum Mechanics * The "Marvelous Moment" * A Quantum Mechanics for Spacetime * What we Need * Sum-Over-Histories Quantum Mechanics for Theories Without a Time * Sum-Over-Spacetime-Histories Quantum Mechanics * Extensions and Contractions * The Construction of Sums Over Spacetime Histories * Some Open Questions * PRACTICAL QUANTUM COSMOLOGY * The Semiclassical Regime * The Semiclassical Approximation
PREFACE: Singular interactions in quantum mechanics: solvable models
Dell'Antonio, Gianfausto; Exner, Pavel; Geyler, Vladimir
2005-06-01
This issue comprises two dozen research papers which are all in one sense or another devoted to models in which the interaction is singular and sharply localized; a typical example is a quantum particle interacting with a family of δ-type potentials. Such an idealization usually makes analysis of their properties considerably easier, sometimes allowing us to reduce it to a simple algebraic problem—this is why one speaks about solvable models. The subject can be traced back to the early days of quantum mechanics; however, the progress in this field was slow and uneven until the 1960s, mostly because singular interactions are often difficult to deal with mathematically and intuitive arguments do not work. After overcoming the initial difficulties the `classical' theory of point interactions was developed, and finally summarized in 1988 in a monograph by Albeverio, Gesztesy, Høegh-Krohn, and Holden, which you will find quoted in numerous places within this issue. A reliable way to judge theories is to observe the progress they make within one or two decades. In this case there is no doubt that the field has witnessed a continuous development and covered areas which nobody had thought of when the subject first emerged. The reader may see it in the second edition of the aforementioned book which was published by AMS Chelsea only recently and contained a brief survey of these new achievements. It is no coincidence that this topical issue appears at the same time; it has been conceived as its counterpart and a forum at which fresh results in the field can demonstrated. Let us briefly survey the contents of the issue. While the papers included have in common the basic subject, they represent a broad spectrum philosophically as well as technically, and any attempt to classify them is somewhat futile. Nevertheless, we will divide them into a few groups. The first comprises contributions directly related to the usual point-interaction ideology. M Correggi and one of the
Quantum mechanics can reduce the complexity of classical models.
Gu, Mile; Wiesner, Karoline; Rieper, Elisabeth; Vedral, Vlatko
2012-03-27
Mathematical models are an essential component of quantitative science. They generate predictions about the future, based on information available in the present. In the spirit of simpler is better; should two models make identical predictions, the one that requires less input is preferred. Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. Here we show how to systematically construct quantum models that break this classical bound, and that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics. This indicates that many observed phenomena could be significantly simpler than classically possible should quantum effects be involved.
The von Neumann model of measurement in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Mello, Pier A. [Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000 México, D. F. (Mexico)
2014-01-08
We describe how to obtain information on a quantum-mechanical system by coupling it to a probe and detecting some property of the latter, using a model introduced by von Neumann, which describes the interaction of the system proper with the probe in a dynamical way. We first discuss single measurements, where the system proper is coupled to one probe with arbitrary coupling strength. The goal is to obtain information on the system detecting the probe position. We find the reduced density operator of the system, and show how Lüders rule emerges as the limiting case of strong coupling. The von Neumann model is then generalized to two probes that interact successively with the system proper. Now we find information on the system by detecting the position-position and momentum-position correlations of the two probes. The so-called 'Wigner's formula' emerges in the strong-coupling limit, while 'Kirkwood's quasi-probability distribution' is found as the weak-coupling limit of the above formalism. We show that successive measurements can be used to develop a state-reconstruction scheme. Finally, we find a generalized transform of the state and the observables based on the notion of successive measurements.
Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
Anderson, E
2006-01-01
Strategies intended to resolve the problem of time in quantum gravity by means of emergent or hidden timefunctions are considered in the arena of relational particle toy models. In situations with `heavy' and `light' degrees of freedom, two notions of emergent semiclassical WKB time emerge; these are furthermore equivalent to two notions of emergent classical `Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach, in a geometric phase formalism, extended to include linear constraints, and with particular care to make explicit those approximations and assumptions used. I propose a new iterative scheme for this in the cosmologically-motivated case with one heavy degree of freedom. I find that the usual semiclassical quantum cosmology emergence of time comes hand in hand with the emergence of other qualitatively significant terms, including back-reactions on the heavy subsystem and second time derivatives. I illustrate my analysis by taking it further for relational particle models with lin...
Effectively Emergent Quantum Mechanics
Exirifard, Qasem
2008-01-01
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently flat. In other words, quantum mechanics might play no role when and where the space-time geometry is highly curved. We study the first two simple models of Effectively Emergent Quantum Mechanics(EEQM): R-dependent EEQM and G-dependent EEQM where R is the Ricci scalar and G is the Gauss-Bonnet Lagrangian density. We discuss that these EEQM theories might be fine tuned to remain consistent with all the implemented experiments and performed observations. In particular, we observe that G-dependent EEQM softens the problem of quantum gravity.
A finite Zitterbewegung model for relativistic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1990-02-19
Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.
Effectively calculable quantum mechanics
Bolotin, Arkady
2015-01-01
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if...
Random matrices as models for the statistics of quantum mechanics
Casati, Giulio; Guarneri, Italo; Mantica, Giorgio
1986-05-01
Random matrices from the Gaussian unitary ensemble generate in a natural way unitary groups of evolution in finite-dimensional spaces. The statistical properties of this time evolution can be investigated by studying the time autocorrelation functions of dynamical variables. We prove general results on the decay properties of such autocorrelation functions in the limit of infinite-dimensional matrices. We discuss the relevance of random matrices as models for the dynamics of quantum systems that are chaotic in the classical limit. Permanent address: Dipartimento di Fisica, Via Celoria 16, 20133 Milano, Italy.
Study of Planar Models in Quantum Mechanics, Field theory and Gravity
Kumar, Sarmistha
2014-01-01
Instantons, monopoles and vortices have become paradigms of topological structures in field theory and quantum mechanics, with important applications in particle physics, astrophysics, condensed matter physics and mathematics. We have discussed here the self-dual Chern-Simons theory specially in (2+1) dimensions. we start with a relevant topological quantum mechanical model (such as Landau problem consisting of two basic chiral oscillators) and extrapolate the analysis to (2+1)dimensional vector field theory. Aspects of selfdual symmetry in topologically massive gravity model were also considered using three different approaches. We have demonstrated how duality symmetric (or chiral) actions are already present in the quantum mechanical examples such as in usual harmonic oscillator. Using the chiral oscillator form, we will briefly develop the key concepts of the soldering mechanism. We have also discussed the non commutative property of such quantum models. Models involving higher order derivative of Abelian...
Fundamentals of quantum mechanics
House, J E
2017-01-01
Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. All required math is clearly explained, including intermediate steps in derivations, and concise review of the math is included in the text at appropriate points. Most of the elementary quantum mechanical models-including particles in boxes, rigid rotor, harmonic oscillator, barrier penetration, hydrogen atom-are clearly and completely presented. Applications of these models to selected “real world” topics are also included. This new edition includes many new topics such as band theory and heat capacity of solids, spectroscopy of molecules and complexes (including applications to ligand field theory), and small molecules of astrophysical interest.
MODEL ANALYSIS AND PARAMETER EXTRACTION FOR MOS CAPACITOR INCLUDING QUANTUM MECHANICAL EFFECTS
Institute of Scientific and Technical Information of China (English)
Hai-yan Jiang; Ping-wen Zhang
2006-01-01
The high frequency CV curves of MOS capacitor have been studied. It is shown that semiclassical model is a good approximation to quantum model and approaches to classical model when the oxide layer is thick. This conclusion provides us an efficient (semiclassical) model including quantum mechanical effects to do parameter extraction for ultrathi noxide device. Here the effective extracting strategy is designed and numerical experiments demonstrate the validity of the strategy.
Noncommutative quantum mechanics
Gamboa, J.; Loewe, M.; Rojas, J. C.
2001-09-01
A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
Energy Technology Data Exchange (ETDEWEB)
Smolyaninov, Igor I., E-mail: smoly@umd.edu
2014-11-15
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear “optical spaces”, such as various geometries necessary for electromagnetic cloaking. Recently we demonstrated that mapping light intensity in a hyperbolic metamaterial may also model the flow of time in an effective (2+1) dimensional Minkowski spacetime. Curving such an effective spacetime creates experimental model of a toy “big bang”. Here we demonstrate that at low light levels this model may be used to emulate a fully covariant version of quantum mechanics in a (2+1) dimensional Minkowski spacetime. When quantum mechanical description is applied near the toy “big bang”, the Everett's “universal wave function” formalism arises naturally, in which the wave function of the model “universe” appears to be a quantum superposition of mutually orthogonal “parallel universe” states.
Nonperturbative contributions in quantum-mechanical models the instantonic approach
Casahorrán, J
2000-01-01
We review the euclidean path-integral formalism in connection with the one-dimensional non-relativistic particle. The configurations which allow to construct a semiclassical approximation classify themselves into either topological (instantons) and non-topological (bounces) solutions. While the instantons dominate the tunneling phenomena between classical vacua, the bounces describe the decay from a false vacuum to the true one. The quantum amplitudes consist on an exponential associated with the classical contribution multiplied by the fluctuation factor which is given by a functional determinant. The eigenfunctions as well as the energy eigenvalues of the quadratic operators at issue can be written in closed form due to the shape-invariance property. Accordingly we resort to the zeta-function method to compute the functional determinants in a systematic way. The effect of the multi-instantons configurations is also carefully considered. To illustrate the instanton calculus in a relevant model we go to the d...
Greiner, Walter
1989-01-01
"Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...
Introduction to quantum mechanics
Villaseñor, Eduardo J. S.
2008-01-01
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
Determinism beneath Quantum Mechanics
Hooft, G
2002-01-01
Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is difficult however is to obtain a Hamiltonian that is bounded from below, and whose ground state is a vacuum that exhibits complicated vacuum fluctuations, as in the real world. Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. This may lead to a sufficiently complex vacuum state, and to an apparent non-locality in the relation between the deterministic ("ontological") states and the quantum states, of the kind needed to explain away the Bell inequalities. Theories of this kind would not only be appealing from a philosophical point of view, but may also be essential for understanding causality at Planckian distance scales.
2011-01-01
We observe a Quantum Brownian Motion (QBM) Model Universe in conjunction with recently established Entanglement Relativity and Parallel Occurrence of Decoherence. The Parallel Occurrence of Decoherence establishes the simultaneous occurrence of decoherence for two mutually irreducible structures (decomposition into subsystems) of the total QBM model universe. First we find that Everett world branching for one structure excludes branching for the alternate structure and in order to reconcile t...
Testing Nonassociative Quantum Mechanics.
Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut
2015-11-27
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Simple one-dimensional quantum-mechanical model for a particle attached to a surface
Energy Technology Data Exchange (ETDEWEB)
Fernandez, Francisco M, E-mail: fernande@quimica.unlp.edu.a [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2010-07-15
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schroedinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(1 0 0). The model is suitable for an advanced undergraduate or graduate course on quantum mechanics.
Advanced Visual Quantum Mechanics
Thaller, Bernd
2005-01-01
Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. It is a self-contained textbook that combines selected topics from atomic physics (spherical symmetry, the hydrogen atom, and particles with spin) with an introduction to quantum information theory (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the strange behavior of Dirac equation solutions. A series of appendices covers important topics from perturbation and scattering theory. The book places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. Though this book stands alone, it can also be paired with Thaller Visual Quantum Mechanics to form a comprehensive course in quantum mechanics. The software for the first book earned the European Academic Software Award 2000 for outstanding innovation in its field.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A complete quantum mechanical model for GaAs/AlGaAs quantum well infrared photodetectors(QWIPs) was presented. The photocurrent was investigated by the optical transition(absorption coefficient)between the ground state and the excited states due to the nonzero component of the radiation field along the sample growth direction. By studying the inter-diffusion of the Al atoms across the GaAs/AlGaAs heterointer faces, the mobility of the drift-diffusion carriers in the excited states was calculated. As a result, the measurement results of the dark current and the photocurrent spectra are explained theoretically.
A Computational Model for Observation in Quantum Mechanics.
1987-03-16
Computer Science Technical Report No. 191, May 1986. [Feynman63j Feynman , R. P., Leighton, R. B., and Sands, M. The Feynman Lectures on Physics...MIT Artificial Intelligence Laboratory Memo 380, Sept. 1976. [Wheeler83] Wheeler , J. A., and Zurek, W. H. Quantum Theory and Measuremrent 72 .4
Wang, Rulin; Zhang, Yu; Bi, Fuzhen; Frauenheim, Thomas; Chen, GuanHua; Yam, ChiYung
2016-07-21
Understanding of the electroluminescence (EL) mechanism in optoelectronic devices is imperative for further optimization of their efficiency and effectiveness. Here, a quantum mechanical approach is formulated for modeling the EL processes in nanoscale light emitting diodes (LED). Based on non-equilibrium Green's function quantum transport equations, interactions with the electromagnetic vacuum environment are included to describe electrically driven light emission in the devices. The presented framework is illustrated by numerical simulations of a silicon nanowire LED device. EL spectra of the nanowire device under different bias voltages are obtained and, more importantly, the radiation pattern and polarization of optical emission can be determined using the current approach. This work is an important step forward towards atomistic quantum mechanical modeling of the electrically induced optical response in nanoscale systems.
Li, Guochang; Chen, George; Li, Shengtao
2016-08-01
Charge transport properties in nanodielectrics present different tendencies for different loading concentrations. The exact mechanisms that are responsible for charge transport in nanodielectrics are not detailed, especially for high loading concentration. A charge transport model in nanodielectrics has been proposed based on quantum tunneling mechanism and dual-level traps. In the model, the thermally assisted hopping (TAH) process for the shallow traps and the tunnelling process for the deep traps are considered. For different loading concentrations, the dominant charge transport mechanisms are different. The quantum tunneling mechanism plays a major role in determining the charge conduction in nanodielectrics with high loading concentrations. While for low loading concentrations, the thermal hopping mechanism will dominate the charge conduction process. The model can explain the observed conductivity property in nanodielectrics with different loading concentrations.
Jensen, L; Swart, Marcel; van Duijnen, Piet Th
2005-01-15
A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By separating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described.
Quantum mechanics in chemistry
Schatz, George C
2002-01-01
Intended for graduate and advanced undergraduate students, this text explores quantum mechanical techniques from the viewpoint of chemistry and materials science. Dynamics, symmetry, and formalism are emphasized. An initial review of basic concepts from introductory quantum mechanics is followed by chapters examining symmetry, rotations, and angular momentum addition. Chapter 4 introduces the basic formalism of time-dependent quantum mechanics, emphasizing time-dependent perturbation theory and Fermi's golden rule. Chapter 5 sees this formalism applied to the interaction of radiation and matt
Quantum mechanics for pedestrians
Pade, Jochen
2014-01-01
This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix coll...
A Quantum Space behind Simple Quantum Mechanics
Directory of Open Access Journals (Sweden)
Chuan Sheng Chew
2017-01-01
Full Text Available In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles. This configuration space (as well as phase space can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.
Quantum cosmological metroland model
Anderson, E.; Franzen, A.T.
2010-01-01
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale
THE QUANTUM – MECHANICAL MODEL OF FORMING CONTACT AREAS IN COMPOSITE MATERIALS WITH SPHERICAL FILLER
Directory of Open Access Journals (Sweden)
E. V. Suhovaya
2011-01-01
Full Text Available The structure and properties of the composites having Fe-C-B-Р binders alloyed with molybdenum and strengthened by the W-C quickly-cooled filler were investigated in this work. The model based on quantum mechanics principles explaining the dependencies of contact interaction zones width on filler diameter was suggested.
Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface
Fernandez, Francisco M.
2010-01-01
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…
Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface
Fernandez, Francisco M.
2010-01-01
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…
Directory of Open Access Journals (Sweden)
Kubicki JD
2000-09-01
Full Text Available Molecular simulations (energy minimizations and molecular dynamics of an n-hexane soot model developed by Smith and co-workers (M. S. Akhter, A. R. Chughtai and D. M. Smith, Appl. Spectrosc., 1985, 39, 143; ref. 1 were performed. The MM+ (N. L. Allinger, J. Am. Chem. Soc., 1977, 395, 157; ref. 2 and COMPASS (H. Sun, J. Phys. Chem., 1998, 102, 7338; ref. 3 force fields were tested for their ability to produce realistic soot nanoparticle structure. The interaction of pyrene with the model soot was simulated. Quantum mechanical calculations on smaller soot fragments were carried out. Starting from an initial 2D structure, energy minimizations are not able to produce the observed layering within soot with either force field. Results of molecular dynamics simulations indicate that the COMPASS force field does a reasonably accurate job of reproducing observations of soot structure. Increasing the system size from a 683 to a 2732 atom soot model does not have a significant effect on predicted structures. Neither does the addition of water molecules surrounding the soot model. Pyrene fits within the soot structure without disrupting the interlayer spacing. Polycyclic aromatic hydrocarbons (PAH, such as pyrene, may strongly partition into soot and have slow desorption kinetics because the PAH-soot bonding is similar to soot–soot interactions. Diffusion of PAH into soot micropores may allow the PAH to be irreversibly adsorbed and sequestered so that they partition slowly back into an aqueous phase causing dis-equilibrium between soil organic matter and porewater.
Dirac, Paul A M
2001-01-01
The author of this concise, brilliant series of lectures on mathematical methods in quantum mechanics was one of the shining intellects in the field, winning a Nobel prize in 1933 for his pioneering work in the quantum mechanics of the atom. Beyond that, he developed the transformation theory of quantum mechanics (which made it possible to calculate the statistical distribution of certain variables), was one of the major authors of the quantum theory of radiation, codiscovered the Fermi-Dirac statistics, and predicted the existence of the positron.The four lectures in this book were delivered
Facing quantum mechanical reality.
Rohrlich, F
1983-09-23
Two recent precision experiments provide conclusive evidence against any local hidden variables theory and in favor of standard quantum mechanics. Therefore the epistemology and the ontology of quantum mechanics must now be taken more seriously than ever before. The consequences of the standard interpretation of quantum mechanics are summarized in nontechnical language. The implications of the finiteness of Planck's constant (h > 0) for the quantum world are as strange as the implications of the finiteness of the speed of light (c < infinity for space and time in relativity theory. Both lead to realities beyond our common experience that cannot be rejected.
Holography and Quantum Mechanics
Wang, X J
2002-01-01
It is illustrated that quantum mechanics can be interpreted as holographic projection of higher dimension classical gravity. In this explanation every quantum path in D-dimension is dual to a classical path of (D+1)-dimension gravity under definite holographic projection. I consider 2-dimension non-relativitic free particle and harmonic oscillator as two examples, and find their gravity dual. I conjecture that every quantum mechanics system has their dual gravity description.
Elementary Nonrelativistic Quantum Mechanics
Rosu, H C
2000-01-01
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different countries. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Gol'dman, I I
2010-01-01
A comprehensive collection of problems of varying degrees of difficulty in nonrelativistic quantum mechanics, with answers and completely worked-out solutions. Among the topics: one-dimensional motion, transmission through a potential barrier, commutation relations, angular momentum and spin, and motion of a particle in a magnetic field. An ideal adjunct to any textbook in quantum mechanics, useful in courses in atomic and nuclear physics, mathematical methods in physics, quantum statistics and applied differential equations. 1961 edition.
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
Nauton, Lionel; Hélaine, Virgil; Théry, Vincent; Hecquet, Laurence
2016-04-12
We propose the first computational model for transketolase (TK), a thiamine diphosphate (ThDP)-dependent enzyme, using a quantum mechanical/molecular mechanical method on the basis of crystallographic TK structures from yeast and Escherichia coli, together with experimental kinetic data reported in the literature with wild-type and mutant TK. This model allowed us to define a new route for ThDP activation in the enzyme environment. We evidenced a strong interaction between ThDP and Glu418B of the TK active site, itself stabilized by Glu162A. The crucial point highlighted here is that deprotonation of ThDP C2 is not performed by ThDP N4' as reported in the literature, but by His481B, involving a HOH688A molecule bridge. Thus, ThDP N4' is converted from an amino form to an iminium form, ensuring the stabilization of the C2 carbanion or carbene. Finally, ThDP activation proceeds via an intermolecular process and not by an intramolecular one as reported in the literature. More generally, this proposed ThDP activation mechanism can be applied to some other ThDP-dependent enzymes and used to define the entire TK mechanism with donor and acceptor substrates more accurately.
O'Sullivan, Colm
2016-03-01
The role of "semi-classical" (Bohr-Sommerfeld) and "semi-quantum-mechanical" (atomic orbital) models in the context of the teaching of atomic theory is considered. It is suggested that an appropriate treatment of such models can serve as a useful adjunct to quantum mechanical study of atomic systems.
Quantum mechanics of leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Mendizabal Cofre, Sebastian
2010-08-15
Leptogenesis is an attractive mechanism that simultaneously explains the matterantimatter asymmetry of the universe as well as the small masses of the standard model neutrinos. This is performed by naturally extending the standard model with the insertion of right handed neutrinos. Leptogenesis is usually studied via the semi-classical Boltzmann equations. However, these equations suffer from basic conceptual problems and they lack to include many quantum phenomena, such as memory effects and coherence oscillations. In order to fully describe leptogenesis, a full quantum treatment is required. In this work we show how to address leptogenesis systematically in a purely quantum way. We start by studying scalar and fermionic excitations in a plasma by solving the Kadanoff-Baym equations of motion for Green's functions, with significant emphasis on the initial and boundary conditions of the solutions. We compute analytically the asymmetry generated from the departure of equilibrium of a particle in a thermal bath. The comparison with the semi-classical Boltzmann approach is also analysed, leading to a qualitative difference between both methods. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry, effects that cannot be studied with the Boltzmann equations. The insertion of standard model interactions like the decay widths for the particles of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes, i.e. we regain the Boltzmann equations. (orig.)
Alvaro, M; Bonilla, L L; Carretero, M; Melnik, R V N; Prabhakar, S
2013-08-21
In this paper we develop a kinetic model for the analysis of semiconductor superlattices, accounting for quantum effects. The model consists of a Boltzmann-Poisson type system of equations with simplified Bhatnagar-Gross-Krook collisions, obtained from the general time-dependent Schrödinger-Poisson model using Wigner functions. This system for superlattice transport is supplemented by the quantum mechanical part of the model based on the Ben-Daniel-Duke form of the Schrödinger equation for a cylindrical superlattice of finite radius. The resulting energy spectrum is used to characterize the Fermi-Dirac distribution that appears in the Bhatnagar-Gross-Krook collision, thereby coupling the quantum mechanical and kinetic parts of the model. The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments. It also allows us to determine more accurately the time-dependent characteristics of superlattices, in particular their current density. Results, for several experimentally grown superlattices, are discussed in the context of self-sustained coherent oscillations of the current density which are important in an increasing range of current and potential applications.
Investigating Student Understanding of Quantum Mechanics Spontaneous Models of Conductivity
Wittmann, M C; Redish, E F; Wittmann, Michael C.; Steinberg, Richard N.; Redish, Edward F.
2002-01-01
Students are taught several models of conductivity, both at the introductory and the advanced level. From early macroscopic models of current flow in circuits, through the discussion of microscopic particle descriptions of electrons flowing in an atomic lattice, to the development of microscopic non-localized band diagram descriptions in advanced physics courses, they need to be able to distinguish between commonly used, though sometimes contradictory, physical models. In investigations of student reasoning about models of conduction, we find that students often are unable to account for the existence of free electrons in a conductor and create models that lead to incorrect predictions and responses contradictory to expert descriptions of the physics. We have used these findings as a guide to creating curriculum materials that we show can be effective helping students to apply the different conduction models more effectively.
Dauger, Dean Edward
2001-08-01
We are successful in building a code that models many particle dynamic quantum systems by combining a semiclassical approximation of Feynman path integrals with parallel computing techniques (particle-in-cell) and numerical methods developed for simulating plasmas, establishing this approach as a viable technique for multiparticle time-dependent quantum mechanics. Run on high-performance parallel computers, this code applies semiclassical methods to simulate the time evolution of wavefunctions of many particles. We describe the analytical derivation and computational implementation of these techniques in detail. We present a study to thoroughly demonstrate the code's fidelity to quantum mechanics, resulting in innovative visualization and analysis techniques. We introduce and exhibit a method to address fermion particle statistics. We present studies of two quantum-mechanical problems: a two-electron, one- dimensional atom, resulting in high-quality extractions of one- and two-electron eigenstates, and electrostatic quasi-modes due to quantum effects in a hot electron plasma, relevant for predictions about stellar evolution. We supply discussions of alternative derivations, alternative implementations of the derivations, and an exploration of their consequences. Source code is shown throughout this dissertation. Finally, we present an extensive discussion of applications and extrapolations of this work, with suggestions for future direction.
Double-slit and electromagnetic models to complete quantum mechanics
De Luca, Jayme
2010-01-01
We analyze a realistic microscopic model for electronic scattering based on the neutral-delay-equations for point charges of the Wheeler-Feynman electrodynamics. We propose a microscopic model according to the electrodynamics of point-charges, complex enough to describe the essential physics. Our microscopic model reaches a simple qualitative agreement with the experimental results as regards interference in double-slit scattering and in electronic scattering by crystals. We discuss our model in the light of existing experimental results, including a qualitative disagreement found for the double-slit experiment. We discuss an approximation for the complex neutral-delay dynamics of our model using piecewise-defined (discontinuous) velocities for all charges and piecewise-constant-velocities for the scattered charge. Our approximation predicts the De Broglie wavelength as an inverse function of the incoming velocity and in the correct order of magnitude. We explain the scattering by crystals in the light of the...
Energy Technology Data Exchange (ETDEWEB)
Yamada, Minoru [Faculty of Electrical and Computer Engineering, Institute of Science and Engineering Kanazawa University, Kakuma-machi, Kanazawa 920-1192 (Japan); Fares, Hesham, E-mail: fares_fares4@yahoo.com [Faculty of Electrical and Computer Engineering, Institute of Science and Engineering Kanazawa University, Kakuma-machi, Kanazawa 920-1192 (Japan); Department of Physics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)
2013-05-01
A generalized theoretical analysis for amplification mechanism in the planar-type Cherenkov laser is given. An electron is represented to be a material wave having temporal and spatial varying phases with finite spreading length. Interaction between the electrons and the electromagnetic (EM) wave is analyzed by counting the quantum statistical properties. The interaction mechanism is classified into the Velocity and Density Modulation (VDM) model and the Energy Level Transition (ELT) model basing on the relation between the wavelength of the EM wave and the electron spreading length. The VDM model is applicable when the wavelength of the EM wave is longer than the electron spreading length as in the microwave region. The dynamic equation of the electron, which is popularly used in the classical Newtonian mechanics, has been derived from the quantum mechanical Schrödinger equation. The amplification of the EM wave can be explained basing on the bunching effect of the electron density in the electron beam. The amplification gain and whose dispersion relation with respect to the electron velocity is given in this paper. On the other hand, the ELT model is applicable for the case that the wavelength of the EM wave is shorter than the electron spreading length as in the optical region. The dynamics of the electron is explained to be caused by the electron transition between different energy levels. The amplification gain and whose dispersion relation with respect to the electron acceleration voltage was derived on the basis of the quantum mechanical density matrix.
Quantum Mechanics interpreted in Quantum Real Numbers
Corbett, J V; Corbett, John V; Durt, Thomas
2002-01-01
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
Josephson junction devices: Model quantum mechanical systems and medical applications
Chen, Josephine
In this dissertation, three experiments using Josephson junction devices are described. In Part I, the effect of dissipation on tunneling between charge states in a superconducting single-electron transistor (sSET) was studied. The sSET was fabricated on top of a semi-conductor heterostructure with a two-dimensional electron gas (2DEG) imbedded beneath the surface. The 2DEG acted as a dissipative ground plane. The sheet resistance of the 2DEG could be varied in situ by applying a large voltage to a gate on the back of the substrate. The zero-bias conductance of the sSET was observed to increase with increasing temperature and 2DEG resistance. Some qualitative but not quantitative agreement was found with theoretical calculations of the functional dependence of the conductance on temperature and 2DEG resistance. Part II describes a series of experiments performed on magnesium diboride point-contact junctions. The pressure between the MgB2 tip and base pieces could be adjusted to form junctions with different characteristics. With light pressure applied between the two pieces, quasiparticle tunneling in superconductor-insulator-superconductor junctions was measured. From these data, a superconducting gap of approximately 2 meV and a critical temperature of 29 K were estimated. Increasing the pressure between the MgB2 pieces formed junctions with superconductor-normal metal-superconductor characteristics. We used these junctions to form MgB2 superconducting quantum interference devices (SQUIDS). Noise levels as low as 35 fT/Hz1/2 and 4 muphi 0/Hz1/2 at 1 kHz were measured. In Part III, we used a SQUID-based instrument to acquire magnetocardiograms (MCG), the magnetic field signal measured from the human heart. We measured 51 healthy volunteers and 11 cardiac patients both at rest and after treadmill exercise. We found age and sex related differences in the MCG of the healthy volunteers that suggest that these factors should be considered when evaluating the MCG for
Noncommutative Quantum Mechanics and Quantum Cosmology
Bastos, Catarina; Dias, Nuno; Prata, Joao Nuno
2009-01-01
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, $\\theta$ and $\\eta$. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Quantum mechanics for mathematicians
Takhtajan, Leon A
2008-01-01
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks ...
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
A quantum mechanical model of the Riemann zeros
Sierra, German
2007-01-01
In 1999 Berry and Keating showed that a regularization of the 1D classical Hamiltonian H = xp gives semiclassically the smooth counting function of the Riemann zeros. In this paper we first generalize this result by considering a phase space delimited by two boundary functions in position and momenta, which induce a fluctuation term in the counting of energy levels. We next quantize the xp Hamiltonian, adding an interaction term that depends on two wave functions associated to the classical boundaries in phase space. The general model is solved exactly, obtaining a continuum spectrum with discrete bound states embbeded in it. We find the boundary wave functions, associated to the Berry-Keating regularization, for which the average Riemann zeros become resonances. A spectral realization of the Riemann zeros is achieved exploiting the symmetry of the model under the exchange of position and momenta which is related to the duality symmetry of the zeta function. The boundary wave functions, giving rise to the Rie...
Quantum mechanical Carnot engine
Bender, C M; Meister, B K
2000-01-01
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
A Soluble Model for Scattering and Decay in Quaternionic Quantum Mechanics I Decay
Horwitz, L P
1994-01-01
The Lee-Friedrichs model has been very useful in the study of decay-scattering systems in the framework of complex quantum mechanics. Since it is exactly soluble, the analytic structure of the amplitudes can be explicitly studied. It is shown in this paper that a similar model, which is also exactly soluble, can be constructed in quaternionic quantum mechanics. The problem of the decay of an unstable system is treated here. The use of the Laplace transform, involving quaternion-valued analytic functions of a variable with values in a complex subalgebra of the quaternion algebra, makes the analytic properties of the solution apparent; some analysis is given of the dominating structure in the analytic continuation to the lower half plane. A study of the corresponding scattering system will be given in a succeeding paper.
Rosu, H C
2000-01-01
This is the first graduate course on elementary quantum mechanics in Internet written in Romanian for the benefit of Romanian speaking students (Romania and Moldova). It is a translation (with corrections) of the Spanish version of the course (physics/9808031, English translation is under consideration), which I did at the request of students of physics in Bucharest. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Dolev, S; Kolenda, N
2005-01-01
For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the most difficult paradoxes known to the human mind. This book represents the combined efforts of sixteen of today's most eminent theoretical physicists to lay out future directions for quantum physics. The authors include Yakir Aharonov, Anton Zeilinger; the Nobel laureates Anthony Leggett and Geradus 't Hooft; Basil Hiley, Lee Smolin and Henry Stapp. Following a foreword by Roger Penrose, the individual chapters address questions such as quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and the possible bearing of quantum phenomena on biology and consciousness.
Nilpotent Symmetries of a Specific N = 2 Supersymmetric Quantum Mechanical Model: A Novel Approach
Krishna, S; Malik, R P
2013-01-01
We derive the on-shell nilpotent supersymmetric (SUSY) transformations for the N = 2 SUSY quantum mechanical model of a one (0 + 1)-dimensional free particle by exploiting the SUSY invariant restrictions on the (anti-)chiral supervariables of the SUSY theory that is defined on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables \\theta and \\bar \\theta with \\theta^2 = \\bar \\theta^2 = 0,\\theta \\bar \\theta + \\bar \\theta \\theta = 0). Within the framework of our novel approach, we express the Lagrangian and conserved SUSY charges in terms of the (anti-)chiral supervariables to demonstrate the SUSY invariance of the Lagrangian and nilpotency of the conserved charges in a simple manner. Our approach has the potential to be generalized to the description of other N = 2 SUSY quantum mechanical systems with physically interesting potential functions.
Brida, Giorgio; Degiovanni, Ivo Pietro; Genovese, Marco; Migdall, Alan; Piacentini, Fabrizio; Polyakov, Sergey V.; Traina, Paolo
2013-03-01
We present the first experimental test that distinguishes between an event-based corpuscular model (EBCM) [H. De Raedt et al.: J. Comput. Theor. Nanosci. 8 (2011) 1052] of the interaction of photons with matter and quantum mechanics. The test looks at the interference that results as a single photon passes through a Mach--Zehnder interferometer [H. De Raedt et al.: J. Phys. Soc. Jpn. 74 (2005) 16]. The experimental results, obtained with a low-noise single-photon source [G. Brida et al.: Opt. Express 19 (2011) 1484], agree with the predictions of standard quantum mechanics with a reduced χ2 of 0.98 and falsify the EBCM with a reduced χ2 of greater than 20.
Brida, Giorgio; Genovese, Marco; Migdall, Alan; Piacentini, Fabrizio; Polyakov, Sergey V; Traina, Paolo
2013-01-01
We present the first experimental test that distinguishes between an event-based corpuscular model (EBCM) [H. De Raedt et al.: J. Comput. Theor. Nanosci. 8 (2011) 1052] of the interaction of photons with matter and quantum mechanics. The test looks at the interference that results as a single photon passes through a Mach-Zehnder interferometer [H. De Raedt et al.: J. Phys. Soc. Jpn. 74 (2005) 16]. The experimental results, obtained with a low-noise single-photon source [G. Brida et al.: Opt. Expr. 19 (2011) 1484], agree with the predictions of standard quantum mechanics with a reduced $\\chi^2$ of 0.98 and falsify the EBCM with a reduced $\\chi^2$ of greater than 20.
Cammi, Roberto
2013-01-01
This Brief presents the main aspects of the response functions theory (RFT) for molecular solutes described within the framework of the Polarizable Continuum Model (PCM). PCM is a solvation model for a Quantum Mechanical molecular system in which the solvent is represented as a continuum distribution of matter. Particular attention is devoted to the description of the basic features of the PCM model, and to the problems characterizing the study of the response function theory for molecules in solution with respect to the analogous theory on isolated molecules.
Mayato, R; Egusquiza, I
2002-01-01
The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multiauthored book, written as an introductory guide for the non-initiated as well as a useful source of information for the expert, covers many of the open questions. A brief historical overview is to be found in the introduction. It is followed by 12 chapters devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This unique monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics.
Quantum Mechanics/Molecular Mechanics Modeling of Enzymatic Processes: Caveats and Breakthroughs.
Quesne, Matthew G; Borowski, Tomasz; de Visser, Sam P
2016-02-18
Nature has developed large groups of enzymatic catalysts with the aim to transfer substrates into useful products, which enables biosystems to perform all their natural functions. As such, all biochemical processes in our body (we drink, we eat, we breath, we sleep, etc.) are governed by enzymes. One of the problems associated with research on biocatalysts is that they react so fast that details of their reaction mechanisms cannot be obtained with experimental work. In recent years, major advances in computational hardware and software have been made and now large (bio)chemical systems can be studied using accurate computational techniques. One such technique is the quantum mechanics/molecular mechanics (QM/MM) technique, which has gained major momentum in recent years. Unfortunately, it is not a black-box method that is easily applied, but requires careful set-up procedures. In this work we give an overview on the technical difficulties and caveats of QM/MM and discuss work-protocols developed in our groups for running successful QM/MM calculations.
Energy Technology Data Exchange (ETDEWEB)
Krishna, S., E-mail: skrishna.bhu@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); Shukla, A., E-mail: ashukla038@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); Malik, R.P., E-mail: rpmalik1995@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); DST-CIMS, Faculty of Science, BHU-Varanasi-221 005 (India)
2014-12-15
Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSY invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.
Probability in quantum mechanics
Directory of Open Access Journals (Sweden)
J. G. Gilson
1982-01-01
Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
Mechanics classical and quantum
Taylor, T T
2015-01-01
Mechanics: Classical and Quantum explains the principles of quantum mechanics via the medium of analytical mechanics. The book describes Schrodinger's formulation, the Hamilton-Jacobi equation, and the Lagrangian formulation. The author discusses the Harmonic Oscillator, the generalized coordinates, velocities, as well as the application of the Lagrangian formulation to systems that are partially or entirely electromagnetic in character under certain conditions. The book examines waves on a string under tension, the isothermal cavity radiation, and the Rayleigh-Jeans result pertaining to the e
Classical and quantum mechanics of the nonrelativistic Snyder model in curved space
Mignemi, S
2011-01-01
The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales beside the speed of light, and is invariant under the action of the de Sitter group. Here, we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS). We discuss the classical and the quantum mechanics of a free particle and of an oscillator in this framework. In analogy with the flat case, the properties of the SdS and aSdS model are rather different. In the SdS case, a lower bound on the localization in position and momentum space exists, which does not arise in the aSdS model. In both cases the energy of the harmonic oscillator acquires a dependence on the frequency, but the quantum mechanical aSdS oscillator admits only a finite numb...
CALL FOR PAPERS: Special Issue on `Singular Interactions in Quantum Mechanics: Solvable Models'
Dell'Antonio, G.; Exner, P.; Geyler, V.
2004-07-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Singular Interactions in Quantum Mechanics: Solvable Models'. This issue should be a repository for high quality original work. We are interested in having the topic interpreted broadly, that is, to include contributions dealing with point-interaction models, one- and many-body, quantum graphs, including graph-like structures coupling different dimensions, interactions supported by curves, manifolds, and more complicated sets, random and nonlinear couplings, etc., as well as approximations helping us to understand the meaning of singular couplings and applications of such models on different parts of quantum mechanics. We believe that when the second printing of the `bible' of the field, the book Solvable Models in Quantum Mechanics by S Albeverio, F Gesztesy, the late R Høegh-Krohn and H Holden, appears it is the right moment to review new developments in this area, with the hope of stimulating further development of these extremely useful techniques. The Editorial Board has invited G Dell'Antonio, P Exner and V Geyler to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are as follows: bullet The subject of the paper should relate to singular interactions in quantum mechanics in the sense described above. bullet Contributions will be refereed and processed according to the usual procedure of the journal. bullet Papers should be original; reviews of a work published elsewhere will not be accepted. The guidelines for the preparation of contributions are as follows: bullet The DEADLINE for submission of contributions is 31 October 2004. This deadline will allow the special issue to appear in about April 2005. bullet There is a nominal page limit of 15 printed pages (approximately 9000 words) per contribution. Papers exceeding these limits may be accepted at the discretion of the Guest Editors. Further advice on
Hidden-variable models for the spin singlet: I. Non-local theories reproducing quantum mechanics
Di Lorenzo, Antonio
2011-01-01
A non-local hidden variable model reproducing the quantum mechanical probabilities for a spin singlet is presented. The non-locality is concentrated in the distribution of the hidden variables. The model otherwise satisfies both the hypothesis of outcome independence, made in the derivation of Bell inequality, and of compliance with Malus's law, made in the derivation of Leggett inequality. It is shown through the prescription of a protocol that the non-locality can be exploited to send information instantaneously provided that the hidden variables can be measured, even though they cannot be controlled.
A Quantitative Model for the Thermocouple Effect Using Statistical and Quantum Mechanics
Bramley, Paul; Clark, Stewart
2003-09-01
This paper employs statistical and quantum mechanics to develop a model for the mechanism underlying the Seebeck effect. The conventional view of the equilibrium criterion for valence electrons in a material is that the Fermi Energy should be constant throughout the system. However, this criterion is an approximation and it is shown to be inadequate for thermocouple systems. An improved equilibrium criterion is developed by applying statistical and quantum mechanics to determine the total flow of electrons across an arbitrary boundary within a system. Dynamic equilibrium is then considered to be the situation where the Fermi Energy either side of the boundary is such that the flow of electrons in each direction is the same. This equilibrium criterion is then applied to the conditions along the thermocouple wires and at the junctions in order to generate a model for the Seebeck effect. The equations involved for calculating the electronic structure of a material cannot be solved analytically, so a solution is achieved using numeric models employing CASTEP code running on a Sun Beowulf cluster and iterative algorithms written in the Excel™ VBA language on a PC. The model is used to calculate the EMF versus temperature function for the gold versus platinum thermocouple, which is then compared with established experimental data.
Quantum Mechanics with Applications
Afnan, Iraj R
2011-01-01
The ebook introduces undergraduate students to the basic skills required to use non-relativistic quantum mechanics for bound and scattering problems in atomic, molecular and nuclear physics. Initial emphasis is on problems that admit analytic solutions. These results are then used in conjunction with symmetry to develop approximation methods for both bound and scattering problems. The text concentrates on the application of computational problems to introduce the basic concepts of quantum mechanics. These are then used to study more complex problems that can be reduced to one-body problems.
Kogan, VI; Gersch, Harold
2011-01-01
Written by a pair of distinguished Soviet mathematicians, this compilation presents 160 lucidly expressed problems in nonrelativistic quantum mechanics plus completely worked-out solutions. Some were drawn from the authors' courses at the Moscow Institute of Engineering, but most were prepared especially for this book. A high-level supplement rather than a primary text, it constitutes a masterful complement to advanced undergraduate and graduate texts and courses in quantum mechanics.The mathematics employed in the proofs of the problems-asymptotic expansions of functions, Green's functions, u
Saxon, David S
2012-01-01
Based on lectures for an undergraduate UCLA course in quantum mechanics, this volume focuses on the formulas of quantum mechanics rather than applications. Widely used in both upper-level undergraduate and graduate courses, it offers a broad self-contained survey rather than in-depth treatments.Topics include the dual nature of matter and radiation, state functions and their interpretation, linear momentum, the motion of a free particle, Schrödinger's equation, approximation methods, angular momentum, and many other subjects. In the interests of keeping the mathematics as simple as possible, m
Hollowood, Timothy J.
2016-07-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.
Time Asymmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Arno R. Bohm
2011-09-01
Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
Experimental Tests of Quantum Mechanics: Pauli Exclusion Principle and Spontaneous Collapse Models
Petrascu, Catalina Curceanu; Bragadireanu, Mario; Clozza, Alberto; Guaraldo, Carlo; Iliescu, Mihai; Rizzo, Alessandro; Vidal, Antonio Romero; Scordo, Alessandro; Sirghi, Diana Laura; Sirghi, Florin; Sperandio, Laura; Doce, Oton Vazquez; Bassi, Angelo; Donadi, Sandro; Milotti, Edoardo; Laubenstein, Matthias; Bertolucci, Sergio; Bragadireanu, Mario; Curceanu, Catalina; Pietreanu, Dorel; Ponta, Titus; Cargnelli, Michael; Ishiwatari, Tomoichi; Marton, Johann; Widmann, Eberhard; Zmeskal, Johann; Matteo, Sergio di; Egger, Jean Pierre
2014-01-01
The Pauli exclusion principle (PEP), as a consequence or the spin-statistics connection, is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, it spurs a lively debate on its possible limits, deeply rooted as it is in the very foundations of Quantum Field Theory. The VIP (VIolation of the Pauli exclusion principle) experiment is searching for a possible small violation of the PEP for electrons, using the method of searching for Pauli Exclusion Principle forbidden atomic transitions in copper. We describe the experimental method and the obtained results; we briefly present future plans to go beyond the actual limit by upgrading the experiment using vetoed new spectroscopic fast Silicon Drift Detectors. We also mention the possibility of using a similar experimental technique to search for possible X-rays generated in the spontaneous collapse models of quantum mechanics.
A set of molecular models based on quantum mechanical ab initio calculations and thermodynamic data
Eckl, Bernhard; Hasse, Hans
2009-01-01
A parameterization strategy for molecular models on the basis of force fields is proposed, which allows a rapid development of models for small molecules by using results from quantum mechanical (QM) ab initio calculations and thermodynamic data. The geometry of the molecular models is specified according to the atom positions determined by QM energy minimization. The electrostatic interactions are modeled by reducing the electron density distribution to point dipoles and point quadrupoles located in the center of mass of the molecules. Dispersive and repulsive interactions are described by Lennard-Jones sites, for which the parameters are iteratively optimized to experimental vapor-liquid equilibrium (VLE) data, i.e. vapor pressure, saturated liquid density, and enthalpy of vaporization of the considered substance. The proposed modeling strategy was applied to a sample set of ten molecules from different substance classes. New molecular models are presented for iso-butane, cyclohexane, formaldehyde, dimethyl...
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Li, Hui; Gordon, Mark S
2007-03-28
A method that combines quantum mechanics (QM), typically a solute, the effective fragment potential (EFP) discrete solvent model, and the polarizable continuum model is described. The EFP induced dipoles and polarizable continuum model (PCM) induced surface charges are determined in a self-consistent fashion. The gradients of these two energies with respect to molecular coordinate changes are derived and implemented. In general, the gradients can be formulated as simple electrostatic forces and torques among the QM nuclei, electrons, EFP static multipoles, induced dipoles, and PCM induced charges. Molecular geometry optimizations can be performed efficiently with these gradients. The formulas derived for EFPPCM can be generally applied to other combined molecular mechanics and continuum methods that employ induced dipoles and charges.
Lonsdale, Richard; Fort, Rachel M; Rydberg, Patrik; Harvey, Jeremy N; Mulholland, Adrian J
2016-06-20
The mechanism of cytochrome P450(CYP)-catalyzed hydroxylation of primary amines is currently unclear and is relevant to drug metabolism; previous small model calculations have suggested two possible mechanisms: direct N-oxidation and H-abstraction/rebound. We have modeled the N-hydroxylation of (R)-mexiletine in CYP1A2 with hybrid quantum mechanics/molecular mechanics (QM/MM) methods, providing a more detailed and realistic model. Multiple reaction barriers have been calculated at the QM(B3LYP-D)/MM(CHARMM27) level for the direct N-oxidation and H-abstraction/rebound mechanisms. Our calculated barriers indicate that the direct N-oxidation mechanism is preferred and proceeds via the doublet spin state of Compound I. Molecular dynamics simulations indicate that the presence of an ordered water molecule in the active site assists in the binding of mexiletine in the active site, but this is not a prerequisite for reaction via either mechanism. Several active site residues play a role in the binding of mexiletine in the active site, including Thr124 and Phe226. This work reveals key details of the N-hydroxylation of mexiletine and further demonstrates that mechanistic studies using QM/MM methods are useful for understanding drug metabolism.
Black holes and quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, G. ' t, E-mail: g.thooft@uu.n [Institute for Theoretical Physics, Utrecht University and Spinoza Institute, P.O. Box 80.195, 3508 TD Utrecht (Netherlands)
2010-07-15
After a brief review of quantum black hole physics, it is shown how the dynamical properties of a quantum black hole may be deduced to a large extent from Standard Model Physics, extended to scales near the Planck length, and combined with results from perturbative quantum gravity. Together, these interactions generate a Hilbert space of states on the black hole horizon, which can be investigated, displaying interesting systematics by themselves. To make such approaches more powerful, a study is made of the black hole complementarity principle, from which one may deduce the existence of a hidden form of local conformal invariance. Finally, the question is raised whether the principles underlying Quantum Mechanics are to be sharpened in this domain of physics as well. There are intriguing possibilities.
Hollowood, Timothy J
2013-01-01
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves evolves according to a stochastic process driven by the unmodified Schrodinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantum measurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.
Quantum mechanics with applications
Beard, David B
2014-01-01
This introductory text emphasizes Feynman's development of path integrals and its application to wave theory for particles. Suitable for undergraduate and graduate students of physics, the well-written, clear, and rigorous text was written by two of the nation's leading authorities on quantum physics. A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. The close relation of quantum theory to physical optics is stressed. Subsequent sections emphasize the physical consequences of a wave theory of material properties, and they offer extensive applications in atomic physics, nuclear physics, solid state physics, and diatomic molecules. Four helpful Appendixes supplement the text.
Epigenetics: Biology's Quantum Mechanics.
Jorgensen, Richard A
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Epigenetics: Biology's Quantum Mechanics
Directory of Open Access Journals (Sweden)
Richard A Jorgensen
2011-04-01
Full Text Available The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920's and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Advanced concepts in quantum mechanics
Esposito, Giampiero; Miele, Gennaro; Sudarshan, George
2015-01-01
Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.
Underwriting information-theoretic accounts of quantum mechanics with a realist, psi-epistemic model
Stuckey, W. M.; Silberstein, Michael; McDevitt, Timothy
2016-05-01
We propose an adynamical interpretation of quantum theory called Relational Blockworld (RBW) where the fundamental ontological element is a 4D graphical amalgam of space, time and sources called a “spacetimesource element.” These are fundamental elements of space, time and sources, not source elements in space and time. The transition amplitude for a spacetimesource element is computed using a path integral with discrete graphical action. The action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy-momentum. This construct of K and J represents an adynamical global constraint between sources, the spacetime metric and the energy-momentum content of the spacetimesource element, rather than a dynamical law for time-evolved entities. To illustrate this interpretation, we explain the simple EPR-Bell and twin-slit experiments. This interpretation of quantum mechanics constitutes a realist, psi-epistemic model that might underwrite certain information-theoretic accounts of the quantum.
Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model
Krishna, S.; Shukla, D.; Malik, R. P.
2016-07-01
In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting 𝒩 = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent 𝒩 = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our 𝒩 = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the 𝒩 = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our 𝒩 = 2 SUSY theory.
Quantum Mechanics and determinism
Hooft, G. 't
2001-01-01
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied to free Maxwell fields. Lorentz invariance is demonstrated.
Transfer of Learning in Quantum Mechanics
Singh, Chandralekha
2016-01-01
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.
Symmetry and quantum mechanics
Corry, Scott
2016-01-01
This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.
Graduate Quantum Mechanics Reform
Carr, L D
2008-01-01
We address four main areas in which graduate quantum mechanics education in the U.S. can be improved: course content; textbook; teaching methods; and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all four of these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, use modern textbooks that include such content, incorporate a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey (QMCS). We find that graduate students respond well to research-based techniques that have previously been tested mainly in introductory courses, and that they learn a great deal of the new content introduced in each ve...
Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence
Harmark, Troels; Orselli, Marta
2014-11-01
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U( N). We show that SMT describes super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the g → ∞ limit of SMT can be mapped to the supersymmetric sector of string theory on AdS5 × S 5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite- N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g = 0 it is a theory of N 2 + 1 harmonic oscillators while for large g it becomes 2 N harmonic oscillators.
Quantum Mechanics in the Infrared
Radicevic, Djordje
2016-01-01
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not a different effective quantum mechanics. Each energy eigenstate of the UV Hamiltonian flows to a probability distribution whose entropy is a natural diagnostic of quantum ergodicity of the original state. These conclusions are supported by various examples worked out in detail.
Memetics of Quantum Mechanical Interpretations
Chakrabarty, I
2006-01-01
Memes, self reproducing mental information and cognitive structures analogous to genes in biology, can be seen as the basis for an explanatory model of cultural and psychological behavior. Their properties and effects are evolutionary conditioned and ultimately seeks to promote their replication. To survive in a context the memes must meet certain conditions. We here propose a Memetics of Quantum Mechanical Interpretations, which have eluded mankind for a century now. We also see how the ideas of memes best fit the way scientific theories in general and Quantum Theory in particular propagates in the scientific brains and finds its expressions in the scientific community and effects the way we perceive Nature.
Basdevant, Jean-Louis
2007-01-01
Beautifully illustrated and engagingly written, Lectures on Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: "If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be 'E = mc2'. Nevertheless, the formula 'E=hV' which was written in the same year 1905 by the same Albert Einstein, and which started quantum theory, concerns their daily life considerably more. In fact, of the three watershed years for physics toward the beginning of the 20th century - 1905: the Special Relativity of Einstein, Lorentz and Poincaré; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the full development of Quantum Mechanics - it is surely the last which has the mos...
Hollowood, Timothy J
2015-01-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generat...
Kongsted, Jacob; Nielsen, Christian B.; Mikkelsen, Kurt V.; Christiansen, Ove; Ruud, Kenneth
2007-01-01
We present a gauge-origin independent method for the calculation of nuclear magnetic shielding tensors of molecules in a structured and polarizable environment. The method is based on a combination of density functional theory (DFT) or Hartree-Fock wave functions with molecular mechanics. The method is unique in the sense that it includes three important properties that need to be fulfilled in accurate calculations of nuclear magnetic shielding constants: (i) the model includes electron correlation effects, (ii) the model uses gauge-including atomic orbitals to give gauge-origin independent results, and (iii) the effect of the environment is treated self-consistently using a discrete reaction-field methodology. The authors present sample calculations of the isotropic nuclear magnetic shielding constants of liquid water based on a large number of solute-solvent configurations derived from molecular dynamics simulations employing potentials which treat solvent polarization either explicitly or implicitly. For both the O17 and H1 isotropic shielding constants the best predicted results compare fairly well with the experimental data, i.e., they reproduce the experimental solvent shifts to within 4ppm for the O17 shielding and 1ppm for the H1 shielding.
Kongsted, Jacob; Nielsen, Christian B; Mikkelsen, Kurt V; Christiansen, Ove; Ruud, Kenneth
2007-01-21
We present a gauge-origin independent method for the calculation of nuclear magnetic shielding tensors of molecules in a structured and polarizable environment. The method is based on a combination of density functional theory (DFT) or Hartree-Fock wave functions with molecular mechanics. The method is unique in the sense that it includes three important properties that need to be fulfilled in accurate calculations of nuclear magnetic shielding constants: (i) the model includes electron correlation effects, (ii) the model uses gauge-including atomic orbitals to give gauge-origin independent results, and (iii) the effect of the environment is treated self-consistently using a discrete reaction-field methodology. The authors present sample calculations of the isotropic nuclear magnetic shielding constants of liquid water based on a large number of solute-solvent configurations derived from molecular dynamics simulations employing potentials which treat solvent polarization either explicitly or implicitly. For both the (17)O and (1)H isotropic shielding constants the best predicted results compare fairly well with the experimental data, i.e., they reproduce the experimental solvent shifts to within 4 ppm for the (17)O shielding and 1 ppm for the (1)H shielding.
Sakurai, Jun John
2011-01-01
This best-selling classic provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts. The author, J. J. Sakurai, was a renowned theorist in particle theory. This revision by Jim Napolitano retains the original material and adds topics that extend the text’s usefulness into the 21st century. The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. You will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell’s inequality. The style and treatment of topics is now more consistent across chapters.
Quantum mechanics and the psyche
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Bananaworld quantum mechanics for primates
Bub, Jeffrey
2016-01-01
What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schro?dinger coined the term "entanglement" to describe these bizarre correlations. Bananaworld -- an imaginary island with "entangled" bananas -- brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding the mysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered...
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Scan Quantum Mechanics: Quantum Inertia Stops Superposition
Gato-Rivera, Beatriz
2015-01-01
A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. leading to...
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Physical microscopic free-choice model in the framework of a Darwinian approach to quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Baladron, Carlos [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47011, Valladolid (Spain)
2017-06-15
A compatibilistic model of free choice for a fundamental particle is built within a general framework that explores the possibility that quantum mechanics be the emergent result of generalised Darwinian evolution acting on the abstract landscape of possible physical theories. The central element in this approach is a probabilistic classical Turing machine -basically an information processor plus a randomiser- methodologically associated with every fundamental particle. In this scheme every system acts not under a general law, but as a consequence of the command of a particular, evolved algorithm. This evolved programme enables the particle to algorithmically anticipate possible future world configurations in information space, and as a consequence, without altering the natural forward causal order in physical space, to incorporate elements to the decision making procedure that are neither purely random nor strictly in the past, but in a possible future. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Towards a Constructive Foundation of Quantum Mechanics
Smilga, Walter
2016-11-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Towards a Constructive Foundation of Quantum Mechanics
Smilga, Walter
2017-01-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Aidas, Kestutis; Kongsted, Jacob; Nielsen, Christian B.; Mikkelsen, Kurt V.; Christiansen, Ove; Ruud, Kenneth
2007-07-01
The theory of a hybrid quantum mechanics/molecular mechanics (QM/MM) approach for gauge-origin independent calculations of the molecular magnetizability using Hartree-Fock or Density Functional Theory is presented. The method is applied to liquid water using configurations generated from classical Molecular Dynamics simulation to calculate the statistical averaged magnetizability. Based on a comparison with experimental data, treating only one water molecule quantum mechanically appears to be insufficient, while a quantum mechanical treatment of also the first solvation shell leads to good agreement between theory and experiment. This indicates that the gas-to-liquid phase shift for the molecular magnetizability is to a large extent of non-electrostatic nature.
On the zigzagging causility model of EPR correlations and on the interpretation of quantum mechanics
de Beauregard, O. Costa
1988-09-01
Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B> = *. The formal parrallelism breaks down at the level of interpretation because (A|C) = ||2. CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is = = , with |Φ> denoting a preparation, |Ψ> a measurement, and U the evolution operator. The transformation |Ψ> = |UΦ> or |Φ> = |U-1Ψ> exchanges the “preparation representation” and the “measurement representation” of a system and is ancillary in the formalization of the quantum chance game by the “wavelike algebra” of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude = Σ between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility = * implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of “blind statistical retrodiction”—that is, of “final cause.”
EOSTA-an improved EOS quantum mechanical model in the STA opacity code
Energy Technology Data Exchange (ETDEWEB)
Bar-Shalom, A. [Koifman 32, Beer-Sheva (Israel) and Artep Inc., Columbia, MD 21045 (United States)]. E-mail: avibs@bgumail.bgu.ac.il; Oreg, J. [Artep Inc., Columbia, MD 21045 (United States); Klapisch, M. [Artep Inc., Columbia, MD 21045 (United States)
2006-05-15
The STA model is extended to include calculations of thermodynamical quantities required for equation of state (EOS). For that purpose the plasma free electrons are now treated quantum mechanically accounting for shape resonances. The resulting gradual orbital ionization assures a regular behavior of all the thermodynamical quantities vs. density and temperature. The relativistic quantum mechanical framework that we have applied in a new code named EOSTA follows Liberman's Inferno model with several improvements that accomplish higher accuracy. These improvements include: a numerical technique to trace all the resonances and follow their detailed structure and application of the phase amplitude method that allows the inclusion of higher angular momenta partial waves and higher energies of the free orbitals. In addition we employ two complementary methods to treat the exchange potential in the calculation of orbital wave functions: (1) for EOS calculations Local Density Approximation is used and (2) for ionization lowering and orbital energies required in the opacity calculations we have found two satisfactory alternatives: (a) the optimized effective potential (OEP) and (b) first order corrected Local Density Approximation. In both alternatives the resulting orbitals are used to calculate the detailed exchange term that includes a proper reduction of the self energy. A new approach for calculating the electronic pressure is presented. The relativistic virial theorem expresses the pressure as a sum of the total energy and a local density term. This form allows consistent calibration of the correlation energy to comply with the periodic table zero pressure density points and higher density pressures. Results are presented describing the various thermodynamical quantities vs. density and temperature in comparison with other calculations and experiments.
Exactly Solvable Quantum Mechanics
Sasaki, Ryu
2014-01-01
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
Chulhai, Dhabih V; Jensen, Lasse
2014-10-01
Raman optical activity has proven to be a powerful tool for probing the geometry of small organic and biomolecules. It has therefore been expected that the same mechanisms responsible for surface-enhanced Raman scattering may allow for similar enhancements in surface-enhanced Raman optical activity (SEROA). However, SEROA has proved to be an experimental challenge and mirror-image SEROA spectra of enantiomers have so far not been measured. There exists a handful of theories to simulate SEROA, all of which treat the perturbed molecule as a point-dipole object. To go beyond these approximations, we present two new methods to simulate SEROA: the first is a dressed-tensors model that treats the molecule as a point-dipole and point-quadrupole object; the second method is the discrete interaction model/quantum mechanical (DIM/QM) model, which considers the entire charge density of the molecule. We show that although the first method is acceptable for small molecules, it fails for a medium-sized one such as 2-bromohexahelicene. We also show that the SEROA mode intensities and signs are highly sensitive to the nature of the local electric field and gradient, the orientation of the molecule, and the surface plasmon frequency width. Our findings give some insight into why experimental SEROA, and in particular observing mirror-image SEROA for enantiomers, has been difficult.
Supersymmetric Quantum Mechanics and Topology
Directory of Open Access Journals (Sweden)
Muhammad Abdul Wasay
2016-01-01
Full Text Available Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Thermodynamic integration from classical to quantum mechanics.
Habershon, Scott; Manolopoulos, David E
2011-12-14
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
Quantum cosmological metroland model
Energy Technology Data Exchange (ETDEWEB)
Anderson, Edward [DAMTP, Cambridge (United Kingdom); Franzen, Anne, E-mail: ea212@cam.ac.u, E-mail: a.t.franzen@uu.n [Spinoza Institute, Utrecht (Netherlands)
2010-02-21
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale of four particles on a line, so that the only physically significant quantities are ratios of relative separations between the constituents' physical objects. Many of our ideas and workings extend to the N-particle case. As such models' configurations resemble depictions of metro lines in public transport maps, we term them 'N-stop metrolands'. This 4-stop model's configuration space is a 2-sphere, from which our metroland mechanics interpretation is via the 'cubic' tessellation. This model yields conserved quantities which are mathematically SO(3) objects like angular momenta but are physically relative dilational momenta (i.e. coordinates dotted with momenta). We provide and interpret various exact and approximate classical and quantum solutions for 4-stop metroland; from these results one can construct expectations and spreads of shape operators that admit interpretations as relative sizes and the 'homogeneity of the model universe's contents', and also objects of significance for the problem of time in quantum gravity (e.g. in the naive Schroedinger and records theory timeless approaches).
Quantum mechanics of materials
Energy Technology Data Exchange (ETDEWEB)
Cohen, M.L.; Heine, V.; Phillips, J.C.
1982-06-01
In the past 25 years, new quantum-mechanical methods have been developed for predicting the configuration of the valence electrons in an atom or an aggregate of many atoms, within the range of energy excitations in which the atoms form interatomic bonds. A theory specifying the configuration of the valence electrons has much to say about the bulk properties of matter that depends on the nature of the interatomic bonds. The new method regards the core electrons and the atomic nucleus as if they constituted a single particle without internal structure. The method is called the pseudopotential theory. A general quantum-mechanical prediction of the properties of a substance in terms of the additive properties of separate chemical bonds is not yet feasible for molecules. However, there is one realm where prediction is now practical: crystalline solids. The regularity of the lattice into which the atoms are organized in a crystal makes it possible to calculate the properties of a macroscopic solid. In other words, many properties of an elemental solid such as lead or a simple binary solid such as gallium arsenide can not be deduced from energy considerations alone. (SC)
Submicroscopic Deterministic Quantum Mechanics
Krasnoholovets, V
2002-01-01
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10^{-28} cm at which three fundamental interactions (electromagnetic, weak, and strong) intersect has been treated as the size of a building block of the space. The appearance of a massive particle is associated with a local deformation of the cellular space, i.e. deformation of a cell. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations called "inertons". The further study has disclosed that inertons are a substructure of the matter waves which are described by the orthodox wave \\psi-function formalism. The c...
An explicit surface-potential-based MOSFET model incorporating the quantum mechanical effects
Basu, Dipanjan; Dutta, Aloke K.
2006-07-01
An explicit surface-potential-based MOSFET model has been proposed in this work here, which takes into account the quantum mechanical effects that arise in deep-submicron MOSFETs. The coupled Schrödinger's and Poisson's equations have been solved by using a variational wave function approach, as proposed by Fang and Howard. The resulting surface potential model is analytical, technology mapped, and completely continuous over the entire range of operation. The surface potential and the inversion charge density calculated using the proposed model show good match with the results of the numerical simulations obtained from a self-consistent Schrödinger-Poisson solver for a wide range of substrate doping and oxide thickness. The simulated values of the drain current match closely with the experimental results published elsewhere. The device small-signal parameters, e.g., transconductance, output conductance, etc., pass the standard benchmark tests suggested by Suyama and Tsividis qualitatively, thereby validating the approach of the model presented.
Biswas, P K; Gogonea, Valentin
2008-10-21
We present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentum-based expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantum-mechanical-molecular-mechanical (QM/MM) calculations, mutual polarization within the QM/MM Hamiltonian can be obtained. We present the mathematical formulation and the analytical expressions for the energy and forces pertaining to the method. We further develop a variational scheme to appropriately determine the expansion coefficients and then validate the method by considering polarizations of ions by the QM system employing the hybrid GROMACS-CPMD QM/MM program. Finally, we present a simpler prescription for adding isotropic polarizability to MM atoms in a QM/MM simulation. Employing this simpler scheme, we present QM/MM energy minimization results for the classic case of a water dimer and a hydrogen sulfide dimer. Also, we present single-point QM/MM results with and without the polarization to study the change in the ionization potential of tetrahydrobiopterin (BH(4)) in water and the change in the interaction energy of solvated BH(4) (described by MM) with the P(450) heme described by QM. The model can be employed for the development of an extensive classical polarizable force-field.
Quantum mechanics using Fradkin's representation
Shajesh, K V; Milton, Kimball A.
2005-01-01
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum mechanics (field theory in one dimension) and apply it to the solution of Schrodinger's equation for the quantum harmonic oscillator.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Modeling of quantum nanomechanics
DEFF Research Database (Denmark)
Jauho, Antti-Pekka; Novotny, Tomas; Donarini, Andrea
2004-01-01
Microelectromechanical systems (MEMS) are approaching the nanoscale, which ultimately implies that the mechanical motion needs to be treated quantum mechanically. In recent years our group has developed theoretical methods to analyze the shuttle transition in the quantum regime (Novotny, 2004...
Quantum Mechanics for Electrical Engineers
Sullivan, Dennis M
2011-01-01
The main topic of this book is quantum mechanics, as the title indicates. It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory. It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions. Two key features make this book different from others on quantum mechanics, even those usually intended for engineers: First, after a brief introduction, much of the development is through Fourier theory, a topic that is at
Geometrical Phases in Quantum Mechanics
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Quantum mechanics the theoretical minimum
Susskind, Leonard
2014-01-01
From the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman’s crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
Factorization Method in Quantum Mechanics
Dong, Shi-Hai
2007-01-01
This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into ...
Decoherence in quantum mechanics and quantum cosmology
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Payton, John L; Morton, Seth M; Moore, Justin E; Jensen, Lasse
2012-06-07
We have derived and implemented analytical gradients for the discrete interaction model/quantum mechanics (DIM/QM) method. DIM/QM combines an atomistic electrodynamics model with time-dependent density functional theory and thus enables modeling of the optical properties for a molecule while taking into account the local environment of a nanoparticle's surface. The DIM/QM analytical gradients allow for geometry optimizations, vibrational frequencies, and Raman spectra to be simulated for molecules interacting with metal nanoparticles. We have simulated the surface-enhanced Raman scattering (SERS) spectra for pyridine adsorbed on different sites of icosahedral nanoparticles with diameters between 1 and 8 nm. To describe the adsorption of the pyridine molecule onto the metal surface, we have implemented a coordination-dependent force field to differentiate the various local surface environments. We find that the DIM/QM method predicts geometries and frequencies that are in good agreement with full QM simulations and experiments. For the simulated SERS spectra of pyridine, we find a significant dependence on the adsorption site and the size of the metal nanoparticle. This illustrates the importance of accounting for the local environment around the molecule. The Raman enhancement factors are shown to roughly mirror the magnitude of the nanoparticle's local field about the molecule. Because the simulated nanoparticles are small, the plasmon peaks are quite broad which results in weak local electric fields and thus modest Raman enhancement factors.
Matrix Quantum Mechanics from Qubits
Hartnoll, Sean A; Mazenc, Edward A
2016-01-01
We introduce a transverse field Ising model with order N^2 spins interacting via a nonlocal quartic interaction. The model has an O(N,Z), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O(N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1+1 dimensional spacetime.
Quantum mechanics II advanced topics
Rajasekar, S
2015-01-01
Quantum Mechanics II: Advanced Topics uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.
Quantum inertia stops superposition: Scan Quantum Mechanics
Gato-Rivera, Beatriz
2017-08-01
Scan Quantum Mechanics is a novel interpretation of some aspects of quantum mechanics in which the superposition of states is only an approximate effective concept. Quantum systems scan all possible states in the superposition and switch randomly and very rapidly among them. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia Iq reaches a critical value Icr for an observable, the switching among its different eigenvalues stops and the corresponding superposition comes to an end, leaving behind a system with a well defined value of that observable. Consequently, increasing the mass, temperature, gravitational strength, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. Moreover, the process could be reversible. Entanglement can only occur between quantum systems because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia Icr corresponding to different observables, which translates into a critical mass Mcr for fixed environmental conditions as well as critical temperatures, critical electric and magnetic fields, etc. In addition, this proposal implies a new radiation mechanism from astrophysical objects with strong gravitational fields, giving rise to non-thermal synchrotron emission, that could contribute to neutron star formation. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
Shen, Lin; Yang, Weitao
2016-04-12
We developed a new multiresolution method that spans three levels of resolution with quantum mechanical, atomistic molecular mechanical, and coarse-grained models. The resolution-adapted all-atom and coarse-grained water model, in which an all-atom structural description of the entire system is maintained during the simulations, is combined with the ab initio quantum mechanics and molecular mechanics method. We apply this model to calculate the redox potentials of the aqueous ruthenium and iron complexes by using the fractional number of electrons approach and thermodynamic integration simulations. The redox potentials are recovered in excellent accordance with the experimental data. The speed-up of the hybrid all-atom and coarse-grained water model renders it computationally more attractive. The accuracy depends on the hybrid all-atom and coarse-grained water model used in the combined quantum mechanical and molecular mechanical method. We have used another multiresolution model, in which an atomic-level layer of water molecules around redox center is solvated in supramolecular coarse-grained waters for the redox potential calculations. Compared with the experimental data, this alternative multilayer model leads to less accurate results when used with the coarse-grained polarizable MARTINI water or big multipole water model for the coarse-grained layer.
Trace anomalies from quantum mechanics
Bastianelli, F; Bastianelli, Fiorenzo; Nieuwenhuizen, Peter van
1993-01-01
The 1-loop anomalies of a d-dimensional quantum field theory can be computed by evaluating the trace of the regulated path integral jacobian matrix, as shown by Fujikawa. In 1983, Alvarez-Gaum\\'e and Witten observed that one can simplify this evaluation by replacing the operators which appear in the regulator and in the jacobian by quantum mechanical operators with the same (anti)commutation relations. By rewriting this quantum mechanical trace as a path integral with periodic boundary conditions for a one-dimensional supersymmetric nonlinear sigma model, they obtained the chiral anomalies for spin 1/2 and 3/2 fields and selfdual antisymmetric tensors in d dimensions. In this article, we treat the case of trace anomalies for spin 0, 1/2 and 1 fields in a gravitational and Yang-Mills background. We do not introduce a supersymmetric sigma model, but keep the original Dirac matrices $\\g^\\m$ and internal symmetry generators $T^a$ in the path integral. As a result, we get a matrix-valued action. Gauge covariance o...
Popper's test of Quantum Mechanics
Bramon, A
2005-01-01
A test of quantum mechanics proposed by K. Popper and dealing with two-particle entangled states emitted from a fixed source has been criticized by several authors. Some of them claim that the test becomes inconclusive once all the quantum aspects of the source are considered. Moreover, another criticism states that the predictions attributed to quantum mechanics in Popper's analysis are untenable. We reconsider these criticisms and show that, to a large extend, the `falsifiability' potential of the test remains unaffected.
The theoretical foundations of quantum mechanics
Baaquie, Belal E
2013-01-01
The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and a...
Sokkar, Pandian; Boulanger, Eliot; Thiel, Walter; Sanchez-Garcia, Elsa
2015-04-14
We present a hybrid quantum mechanics/molecular mechanics/coarse-grained (QM/MM/CG) multiresolution approach for solvated biomolecular systems. The chemically important active-site region is treated at the QM level. The biomolecular environment is described by an atomistic MM force field, and the solvent is modeled with the CG Martini force field using standard or polarizable (pol-CG) water. Interactions within the QM, MM, and CG regions, and between the QM and MM regions, are treated in the usual manner, whereas the CG-MM and CG-QM interactions are evaluated using the virtual sites approach. The accuracy and efficiency of our implementation is tested for two enzymes, chorismate mutase (CM) and p-hydroxybenzoate hydroxylase (PHBH). In CM, the QM/MM/CG potential energy scans along the reaction coordinate yield reaction energies that are too large, both for the standard and polarizable Martini CG water models, which can be attributed to adverse effects of using large CG water beads. The inclusion of an atomistic MM water layer (10 Å for uncharged CG water and 5 Å for polarizable CG water) around the QM region improves the energy profiles compared to the reference QM/MM calculations. In analogous QM/MM/CG calculations on PHBH, the use of the pol-CG description for the outer water does not affect the stabilization of the highly charged FADHOOH-pOHB transition state compared to the fully atomistic QM/MM calculations. Detailed performance analysis in a glycine-water model system indicates that computation times for QM energy and gradient evaluations at the density functional level are typically reduced by 40-70% for QM/MM/CG relative to fully atomistic QM/MM calculations.
Principles of Quantum Mechanics
Landé, Alfred
2013-10-01
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Discovering Quantum Mechanics Once Again
Duck, Ian M
2003-01-01
We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend' Heisenberg who seeks to construct a dynamical theory of probabilities and is lead -- seemingly inevitably -- to the Principles of Quantum Mechanics.
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Quantum mechanics of molecular structures
Yamanouchi, Kaoru
2012-01-01
At a level accessible to advanced undergraduates, this textbook explains the fundamental role of quantum mechanics in determining the structure, dynamics, and other properties of molecules. Readers will come to understand the quantum-mechanical basis for harmonic oscillators, angular momenta and scattering processes. Exercises are provided to help readers deepen their grasp of the essential phenomena.
"Electronium": A Quantum Atomic Teaching Model.
Budde, Marion; Niedderer, Hans; Scott, Philip; Leach, John
2002-01-01
Outlines an alternative atomic model to the probability model, the descriptive quantum atomic model Electronium. Discusses the way in which it is intended to support students in learning quantum-mechanical concepts. (Author/MM)
Watanabe, Hiroshi C; Kubillus, Maximilian; Kubař, Tomáš; Stach, Robert; Mizaikoff, Boris; Ishikita, Hiroshi
2017-07-21
In the condensed phase, quantum chemical properties such as many-body effects and intermolecular charge fluctuations are critical determinants of the solvation structure and dynamics. Thus, a quantum mechanical (QM) molecular description is required for both solute and solvent to incorporate these properties. However, it is challenging to conduct molecular dynamics (MD) simulations for condensed systems of sufficient scale when adapting QM potentials. To overcome this problem, we recently developed the size-consistent multi-partitioning (SCMP) quantum mechanics/molecular mechanics (QM/MM) method and realized stable and accurate MD simulations, using the QM potential to a benchmark system. In the present study, as the first application of the SCMP method, we have investigated the structures and dynamics of Na(+), K(+), and Ca(2+) solutions based on nanosecond-scale sampling, a sampling 100-times longer than that of conventional QM-based samplings. Furthermore, we have evaluated two dynamic properties, the diffusion coefficient and difference spectra, with high statistical certainty. Furthermore the calculation of these properties has not previously been possible within the conventional QM/MM framework. Based on our analysis, we have quantitatively evaluated the quantum chemical solvation effects, which show distinct differences between the cations.
On Finite $J$-Hermitian Quantum Mechanics
Lee, Sungwook
2014-01-01
In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.
Modern Approach to Quantum Mechanics
Townsend, John S.
Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics lets professors expose their undergraduates to the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new: Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems gives students something new and interesting while providing elegant but straightforward examples of the essential structure of quantum mechanics. When wave mechanics is introduced later, students perceive it correctly as only one aspect of quantum mechanics and not the core of the subject. Praised for its pedagogical brilliance, clear writing, and careful explanations, this book is destined to become a landmark text.
Hidden scale in quantum mechanics
Giri, Pulak Ranjan
2007-01-01
We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through the nontrivial boundary conditions. We discuss a couple of classically scale invariant free particle systems to illustrate the issue. In this context it has been shown that a free quantum particle moving on a full line may have localized wave-packet around the origin. As a generalization, it has also been shown that particles moving on a portion of a plane or on a portion of a three dimensional space can have unusual localized wave-packet.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A complete quantum mechanical model for GaAs/AlGaAs quantum well infrared photodetectors(QWIPs) is presented here. The model consisted of four parts: (1) Starting with the description of the electromagnetic field of the infrared radiation in the QWIP, effective component of the vector potential 〈|Az|〉 along the QWIP growth direction (z-axis) due to the optical diffraction grating was calculated. (2) From the wave transmissions and the occupations of the electronic states, it was discussed that the dark current in the QWIP is determined by the drift-diffusion current of carriers thermally excited from the ground sublevel in the quantum well to extended states above the barrier. (3) The photocurrent was investigated by the optical transition (absorption coefficient between the ground state to excited states due to the nonzero-〈|Az|〉 ). (4) By studying the inter-diffusion of the Al atoms across the GaAs/AlGaAs heterointerfaces,the mobility of the drift-diffusion carriers in the excited states was calculated, so the measurement results of the dark current and photocurrent spectra can be explained theoretically. With the complete quantum mechanical descriptions of (1-4), QWIP device design and optimization are possible.
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Tapas, E-mail: tapas.mukherjee1@gmail.co [Physics Department, Bhairab Ganguly College, Kolkata-700056 (India); Dutta, Dhanadeep [Radiochemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai-400085 (India)
2010-07-15
In the bubble model of positronium annihilation in liquids, the inward contractile force on the bubble surface is described through classical surface tension of the liquids. In the present calculation, we adopted a simple quantum mechanical approach to describe the bubble surface energy in terms of the motion of a representative quasi-free electron outside the bubble. The bubble parameters (radius, potential, etc.) for different liquids obtained using the prescribed model are consistent with the results obtained using classical surface tension.
Mathematical foundation of quantum mechanics
Parthasarathy, K R
2005-01-01
This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...
Quantum mechanics a modern development
Ballentine, Leslie E
2015-01-01
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory. In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions ...
Communication: quantum mechanics without wavefunctions.
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed.
Coherent states in quantum mechanics
Rodrigues, R D L; Fernandes, D
2001-01-01
We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.
Horizon quantum mechanics of rotating black holes
Energy Technology Data Exchange (ETDEWEB)
Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Giugno, Andrea [Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Giusti, Andrea [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Micu, Octavian [Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele (Romania)
2017-05-15
The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. (orig.)
Fun with supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
Quantum Mechanics of Extended Objects
Sastry, R R
2000-01-01
We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this representation is used to demonstrate the quantization of spacetime. The quantum mechanics of extended objects is then applied to two paradigm examples, the fuzzy (extended object) harmonic oscillator and the Yukawa potential. In the second example the phenomenological coupling constant of the $\\omega$ meson which mediates the short range and repulsive nucleon force as well as the repulsive core radius are theoretically predicted.
Quantum mechanics in Hilbert space
Prugovecki, Eduard
2006-01-01
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the
Linear operators for quantum mechanics
Jordan, Thomas F
2006-01-01
This compact treatment highlights the logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in the mathematics of linear operators.Originally oriented toward atomic physics, quantum mechanics became a basic language for solid-state, nuclear, and particle physics. Its grammar consists of the mathematics of linear operators, and with this text, students will find it easier to understand and use the language of physics. Topics include linear spaces and linear fun
Experimental status of quaternionic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Brumby, S.P.; Joshi, G.C.
1995-10-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. The only direct search for quaternionic quantum mechanics yet carried out is reviewed and is proposed to look for quaternionic effects in correlated multi-particle systems. It is also discussed how such experiments might distinguish between the several quaternionic models proposed in the literature. 21 refs.
Some Mutant Forms of Quantum Mechanics
Takeuchi, Tatsu; Lewis, Zachary; Minic, Djordje
2013-01-01
We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.
Stochastic methods in quantum mechanics
Gudder, Stanley P
2005-01-01
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
Quantum mechanical irreversibility and measurement
Grigolini, P
1993-01-01
This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will
Time Asymmetric Quantum Mechanics
National Research Council Canada - National Science Library
Arno R Bohm; Manuel Gadella; Piotr Kielanowski
2011-01-01
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1...
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Analytical mechanics for relativity and quantum mechanics
Johns, Oliver Davis
2011-01-01
Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...
Quantum mechanics in complex systems
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Superconducting Qubits as Mechanical Quantum Engines
Sachtleben, Kewin; Mazon, Kahio T.; Rego, Luis G. C.
2017-09-01
We propose the equivalence of superconducting qubits with a pistonlike mechanical quantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.
Hilbert space and quantum mechanics
Gallone, Franco
2015-01-01
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...
Quantum mechanics principles and formalism
McWeeny, Roy
2012-01-01
Focusing on main principles of quantum mechanics and their immediate consequences, this graduate student-oriented volume develops the subject as a fundamental discipline, opening with review of origins of Schrödinger's equations and vector spaces.
Quantum mechanical description of waveguides
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong; He Bing
2008-01-01
Applying the spinor representation of the electromagnetic field,this paper present a quantum-mechanical description of waveguides.As an example of application,a potential qubit generated by photon tunnelling is discussed.
Quantum Mechanics and Common Sense
Gantsevich, S V
2016-01-01
A physical picture for Quantum Mechanics which permits to conciliate it with the usual common sense is proposed. The picture agrees with the canonical Copenhagen interpretation making more clear its statements.
Quantum mechanics I the fundamentals
Rajasekar, S
2015-01-01
Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems.
A Quantum Space Behind Simple Quantum Mechanics
Chew, Chuan Sheng; Payne, Jason
2016-01-01
In physics, we are supposed to learn from experiments what constitutes a good/correct theoretical/mathematical model of any physical concept, the physical space should not be an exception. The best picture of the physical space, in Newtonian physics, is given by the configuration space of a free particle. The space, as well as the phase space, can be constructed as a representation space of the relativity symmetry. Starting with the corresponding quantum symmetry, we illustrate the construction of a quantum space along the lines of the quantum phase space and demonstrate the retrieval of the classical picture as an approximation through the contraction of the (relativity) symmetry and the representations of it. The result suggests a picture of the physical space beyond that of a finite dimensional manifold.
The physics of quantum mechanics
Binney, James
2014-01-01
The Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. It shows that the theory follows naturally from the use of probability amplitudes to derive probabilities. It stresses that stationary states are unphysical mathematical abstractions that enable us to solve the theory's governing equation, the time-dependent Schroedinger equation. Every opportunity is taken to illustrate the emergence of the familiarclassical, dynamical world through the quantum interference of stationary states. The text stresses the continuity be
Institute of Scientific and Technical Information of China (English)
Claude Pouchan; Philippe Carbonniere
2009-01-01
We present quantum mechanical vibrational computations beyond the harmonic approximation from effective second order perturbative and variation perturbation treatments defined as static approaches, as well as vibrational analysis from density functional theory molecular dynamics trajectories at 300 and 600 K. The four schemes are compared in terms of prediction of fundamental transitions, and simulation of the corresponding medium infrared spectrum at the same level of theory using the B3LYP/6-31+G(d,p) description of the electronic structure. We summarize conclusions about advantages and drawbacks of these two approaches and report the main results obtained for semi-rigid and flexible molecules.
Jorgensen, PET
1987-01-01
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
A study of quantum mechanical probabilities in the classical Hodgkin-Huxley model.
Moradi, N; Scholkmann, F; Salari, V
2015-03-01
The Hodgkin-Huxley (HH) model is a powerful model to explain different aspects of spike generation in excitable cells. However, the HH model was proposed in 1952 when the real structure of the ion channel was unknown. It is now common knowledge that in many ion-channel proteins the flow of ions through the pore is governed by a gate, comprising a so-called "selectivity filter" inside the ion channel, which can be controlled by electrical interactions. The selectivity filter (SF) is believed to be responsible for the selection and fast conduction of particular ions across the membrane of an excitable cell. Other (generally larger) parts of the molecule such as the pore-domain gate control the access of ions to the channel protein. In fact, two types of gates are considered here for ion channels: the "external gate", which is the voltage sensitive gate, and the "internal gate" which is the selectivity filter gate (SFG). Some quantum effects are expected in the SFG due to its small dimensions, which may play an important role in the operation of an ion channel. Here, we examine parameters in a generalized model of HH to see whether any parameter affects the spike generation. Our results indicate that the previously suggested semi-quantum-classical equation proposed by Bernroider and Summhammer (BS) agrees strongly with the HH equation under different conditions and may even provide a better explanation in some cases. We conclude that the BS model can refine the classical HH model substantially.
Phillips, Kathy L; Di Toro, Dominic M; Sandler, Stanley I
2011-02-01
The soil sorption coefficient, K(OC), is an important property affecting the environmental fate of organic molecules. Difficulties associated with measuring K(OC) have led to many attempts to predict this property, but most rely on empirical descriptors for the soil phase determined from correlations with measured K(OC) data, and are thereby limited by the data quality and diversity. A new method is presented to predict K(OC) for nonionic organic compounds that requires only molecular structures. No calibration is performed. Using model humic acid (HA) and fulvic acid (FA) molecular structures from the literature, the soil organic matter is modeled as an organic solvent composed of HA or FA molecules. K(OC) is predicted as an organic solvent-water partition coefficient using the quantum mechanics-based model COSMO-SAC. The log K(OC) values for a set of 440 diverse, environmentally relevant chemicals are predicted with a root-mean-square error of 0.84-1.08, depending on which model HA or FA is used.
Quantum mechanics in a nutshell
Mahan, Gerald D
2009-01-01
Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original
A Soluble Model for Scattering and Decay in Quaternionic Quantum Mechanics II Scattering
Horwitz, L P
1994-01-01
In a previous paper, it was shown that a soluble model can be constructed for the description of a decaying system in analogy to the Lee-Friedrichs model of complex quantum theory. It is shown here that this model also provides a soluble scattering theory, and therefore constitutes a model for a decay scattering system. Generalized second resolvent equations are obtained for quaternionic scattering theory. It is shown explicitly for this model, in accordance with a general theorem of Adler, that the scattering matrix is complex subalgebra valued. It is also shown that the method of Adler, using an effective optical potential in the complex sector to describe the effect of the quaternionic interactions, is equivalent to the general method of Green's functions described here.
Mathematical foundations of quantum mechanics
Mackey, George W
2004-01-01
Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University.Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum
Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
Harmark, Troels
2014-01-01
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transit...
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
Liu, Haiyan; Lu, Zhenyu; Cisneros, G Andres; Yang, Weitao
2004-07-08
The determination of reaction paths for enzyme systems remains a great challenge for current computational methods. In this paper we present an efficient method for the determination of minimum energy reaction paths with the ab initio quantum mechanical/molecular mechanical approach. Our method is based on an adaptation of the path optimization procedure by Ayala and Schlegel for small molecules in gas phase, the iterative quantum mechanical/molecular mechanical (QM/MM) optimization method developed earlier in our laboratory and the introduction of a new metric defining the distance between different structures in the configuration space. In this method we represent the reaction path by a discrete set of structures. For each structure we partition the atoms into a core set that usually includes the QM subsystem and an environment set that usually includes the MM subsystem. These two sets are optimized iteratively: the core set is optimized to approximate the reaction path while the environment set is optimized to the corresponding energy minimum. In the optimization of the core set of atoms for the reaction path, we introduce a new metric to define the distances between the points on the reaction path, which excludes the soft degrees of freedom from the environment set and includes extra weights on coordinates describing chemical changes. Because the reaction path is represented by discrete structures and the optimization for each can be performed individually with very limited coupling, our method can be executed in a natural and efficient parallelization, with each processor handling one of the structures. We demonstrate the applicability and efficiency of our method by testing it on two systems previously studied by our group, triosephosphate isomerase and 4-oxalocrotonate tautomerase. In both cases the minimum energy paths for both enzymes agree with the previously reported paths.
The quantum field theory interpretation of quantum mechanics
de la Torre, Alberto C.
2015-01-01
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Quantum Mechanics and Narratability
Myrvold, Wayne C.
2016-07-01
As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.
Oss, Stefano; Rosi, Tommaso
2015-04-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
Quantum mechanics without potential function
Energy Technology Data Exchange (ETDEWEB)
Alhaidari, A. D., E-mail: haidari@sctp.org.sa [Saudi Center for Theoretical Physics, P.O. Box 32741, Jeddah 21438 (Saudi Arabia); Ismail, M. E. H. [Department of Mathematics, University of Central Florida, Orlando, Florida 32816 (United States)
2015-07-15
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
2007-07-20
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Kuechler, Erich R.
Molecular modeling and computer simulation techniques can provide detailed insight into biochemical phenomena. This dissertation describes the development, implementation and parameterization of two methods for the accurate modeling of chemical reactions in aqueous environments, with a concerted scientific effort towards the inclusion of charge-dependent non-bonded non-electrostatic interactions into currently used computational frameworks. The first of these models, QXD, modifies interactions in a hybrid quantum mechanical/molecular (QM/MM) mechanical framework to overcome the current limitations of 'atom typing' QM atoms; an inaccurate and non-intuitive practice for chemically active species as these static atom types are dictated by the local bonding and electrostatic environment of the atoms they represent, which will change over the course of the simulation. The efficacy QXD model is demonstrated using a specific reaction parameterization (SRP) of the Austin Model 1 (AM1) Hamiltonian by simultaneously capturing the reaction barrier for chloride ion attack on methylchloride in solution and the solvation free energies of a series of compounds including the reagents of the reaction. The second, VRSCOSMO, is an implicit solvation model for use with the DFTB3/3OB Hamiltonian for biochemical reactions; allowing for accurate modeling of ionic compound solvation properties while overcoming the discontinuous nature of conventional PCM models when chemical reaction coordinates. The VRSCOSMO model is shown to accurately model the solvation properties of over 200 chemical compounds while also providing smooth, continuous reaction surfaces for a series of biologically motivated phosphoryl transesterification reactions. Both of these methods incorporate charge-dependent behavior into the non-bonded interactions variationally, allowing the 'size' of atoms to change in meaningful ways with respect to changes in local charge state, as to provide an accurate, predictive and
Why bouncing droplets are a pretty good model of quantum mechanics
Brady, Robert
2014-01-01
In 2005, Couder, Protiere, Fort and Badouad showed that oil droplets bouncing on a vibrating tray of oil can display nonlocal interactions reminiscent of the particle-wave associations in quantum mechanics; in particular they can move, attract, repel and orbit each other. Subsequent experimental work by Couder, Fort, Protiere, Eddi, Sultan, Moukhtar, Rossi, Molacek, Bush and Sbitnev has established that bouncing drops exhibit single-slit and double-slit diffraction, tunnelling, quantised energy levels, Anderson localisation and the creation/annihilation of droplet/bubble pairs. In this paper we explain why. We show first that the surface waves guiding the droplets are Lorentz covariant with the characteristic speed c of the surface waves; second, that pairs of bouncing droplets experience an inverse-square force of attraction or repulsion according to their relative phase, and an analogue of the magnetic force; third, that bouncing droplets are governed by an analogue of Schroedinger's equation where Planck's...
Photodissociation of HBr/LiF(001): A quantum mechanical model
Seideman, Tamar
1993-01-01
The photodissociation dynamics of HBr adsorbed on a LiF(001) surface is studied using time-independent quantum mechanics. The photodissociation lineshape and the Br(P(sub 1/2)-2)/Br(P(sub 3/2)-2) yield ratio are computed and compared with the corresponding quantities for gas phase photodissociation. The angular distribution of the hydrogen photofragments following excitation of adsorbed HBr is computed and found to agree qualitatively with experimental data. The effect of polarization of the photon is illustrated and discussed. The field polarization is found to affect significantly the magnitude of the photodissociation signal but not the angular dependence of the photofragment distribution, in agreement with experiment and in accord with expectations for a strongly aligned adsorbed phase.
Photodissociation of HBr/LiF(001) - A quantum mechanical model
Seideman, Tamar
1993-01-01
The photodissociation dynamics of HBr adsorbed on an LiF(001) surface is studied using time-independent quantum mechanics. The photodissociation line shape and the Br(2P(1/2))/Br(2P(3/2)) yield ratio are computed and compared with the corresponding quantities for gas phase photodissociation. The angular distribution of the hydrogen photofragments following excitation of adsorbed HBr is computed and found to agree qualitatively with experimental data. The effect of polarization of the photon is illustrated and discussed. We find the field polarization to affect significantly the magnitude of the photodissociation signal but not the angular dependence of the photofragment distribution, in agreement with experiment and in accord with expectations for a strongly aligned adsorbed phase.
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Non-relativistic quantum mechanics
Puri, Ravinder R.
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.
Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C
2015-08-28
According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.
Framing difficulties in quantum mechanics
Modir, Bahar; Sayre, Eleanor C
2016-01-01
Students' difficulties in quantum mechanics may be the result of unproductive framing and not fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of the epistemological framing, we investigated four frames in our observational data: algorithmic math, conceptual math, algorithmic physics, and conceptual physics. We then used our framework to seek an underlying structure to the long lists of published difficulties that span many topics in quantum mechanics. We mapped descriptions of published difficulties into errors in epistemological framing and resource use. We analyzed descriptions of students' problem solving to find their frames, and compared students' framing to framing (and frame shifting) required by problem statements. We found three categories of error: mismatches between students' framing and problem statement framing; inappropriate or absent transiti...
Algebraic Quantum Mechanics and Pregeometry
Hiley, D J B P G D B J
2006-01-01
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
Nilpotent Quantum Mechanics: Analogs and Applications
Directory of Open Access Journals (Sweden)
Peter Marcer
2017-07-01
Full Text Available The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state and its environment (vacuum are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This zero square-root construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on “The ‘Logic’ of Self-Organizing Systems” [1], in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.
Remarks on osmosis, quantum mechanics, and gravity
Carroll, Robert
2011-01-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Quantum mechanics foundations and applications
Swanson, Donald Gary
2006-01-01
Progressing from the fundamentals of quantum mechanics (QM) to more complicated topics, Quantum Mechanics: Foundations and Applications provides advanced undergraduate and graduate students with a comprehensive examination of many applications that pertain to modern physics and engineering.Based on courses taught by the author, this textbook begins with an introductory chapter that reviews historical landmarks, discusses classical theory, and establishes a set of postulates. The next chapter demonstrates how to find the appropriate wave functions for a variety of physical systems in one dimens
Effective equations for the quantum pendulum from momentous quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Morton, Seth Michael; Jensen, Lasse
2010-08-21
A new polarizable quantum mechanics/molecular mechanics method for the calculation of response properties of molecules adsorbed on metal nanoparticles is presented. This method, which we denote the discrete interaction model/quantum mechanics (DIM/QM) method, represents the nanoparticle atomistically which enables the modeling of the influence of the local environment of a nanoparticle surface on the optical properties of a molecule. Using DIM/QM, we investigate the excitation energies of rhodamine-6G (R6G) and crystal violet (CV) adsorbed on silver and gold nanoparticles of different quasispherical shapes and sizes. The metal nanoparticle is characterized by its static total polarizability, a reasonable approximation for frequencies far from the plasmon resonance. We observe that for both R6G and CV, the presence of the nanoparticle shifts the strongest excitation to the red approximately 40 nm and also increases the oscillator strength of that excitation. The shifts in excitation energies due to the nanoparticle surface are found to be comparable to those due to solvation. We find that these shifts decay quickly as the molecule is moved away from the surface. We also find that the wavelength shift is largest when the transition dipole moment is aligned with the edges of the nanoparticle surface where the electric field is expected to be the largest. These results show that the molecular excitations are sensitive to the local environment on the nanoparticle as well as the specific orientation of the molecule relative to the surface.
Institute of Scientific and Technical Information of China (English)
SHALINI Mehta; YOGEESWARI Perumal; SRIRAM Dharmarajan; INDUJA Sridharan
2007-01-01
Objective: To study the effect of halo substitution on disubstituted aryl semicarbazones on the anticonvulsant potential and model the activity based on quantum mechanics. Methods: A series of twenty-six compounds of N4-(4-bromo-3-methylphenyl) semicarbazones were synthesized and evaluated for the anticonvulsant activity in the maximal electroshock seizure (MES) and subcutaneous pentylenetetrazole (scPTZ) seizure threshold tests. Some potential compounds were also tested in the subcutaneous strychnine (scSTY) and subcutaneous picrotoxin (scPIC) seizure threshold tests. The synthesized compounds were tested for behavioral impairment and CNS (central nervous system) depression in mice. Quantum mechanical modelling was carried out on these compounds to gain understanding on the structural features essential for activity. Results: Some compounds possessed broad spectrum anticonvulsant activity as indicated by their effect in pentylenetetrazole, strychnine, picrotoxin and maximal electroshock seizures models in resemblance to other aryl semicarbazone derivatives reported earlier. The higher the difference in HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy levels was, the greater was the activity profile. Conclusion: The pharmacophoric requirements for compounds to exhibit anticonvulsant activity that includes one aryl unit in proximity to a hydrogen donor-acceptor domain and an electron donor have been justified with the molecular orbital surface analysis of the synthesized compounds.
The cellular automaton interpretation of quantum mechanics
't Hooft, Gerard
2016-01-01
This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The book presents examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of...
Quantum Mechanics, is it magic
Ferrero, M; Sánchez-Gómez, J L
2008-01-01
We show that quantum mechanics is the first theory in human history that violates the basic a priori principles that have shaped human thought since immemorial times. Therefore although it is more contrary to magic than any body of knowledge could be, what could be called its magic precisely resides in this violation.
Mind, matter and quantum mechanics
Stapp, Henry P
2009-01-01
"Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter," writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the "orthodox" interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questi...
Philosophic foundations of quantum mechanics
Reichenbach, Hans
1998-01-01
Physics concerns direct analysis of the physical world, while philosophy analyzes knowledge about the physical world. This volume combines both disciplines for a philosophical interpretation of quantum physics - an interpretation free from the imprecision of metaphysics, offering a view of the atomic world and its quantum mechanical results as concrete as the visible everyday world.Written by an internationally renowned philosopher who specialized in symbolic logic and the theory of relativity, this approach consists of three parts. The first section, which requires no background in math or p
Operator methods in quantum mechanics
Schechter, Martin
2003-01-01
This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q
Wigner distributions in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ercolessi, E; Marmo, G; Morandi, G; Mukunda, N [Physics Department, University of Bologna, INFN and CNISM. 46 v.Irnerio. I-40126, Bologna (Italy); Dip. di Scienze Fisiche. University di Napoli ' Federico II' and INFN. v.Cinzia. I-80100 Naples (Italy); Physics Department, University of Bologna, INFN and CNISM. 6/2 v.le Berti Pichat. I-40127, Bologna (Italy); Centre for High-Energy Physics. Indian Institute of Science. Bamgalore 560012 (India)
2007-11-15
The Weyl-Wigner description of quantum mechanical operators and states in classical phase-space language is well known for Cartesian systems. We describe a new approach based on ideas of Dirac which leads to the same results but with interesting additional insights. A way to set up Wigner distributions in an interesting non-Cartesian case, when the configuration space is a compact connected Lie group, is outlined. Both these methods are adapted to quantum systems with finite-dimensional Hilbert spaces, and the results are contrasted.
Paradoxical reflection in quantum mechanics
Pedro L. Garrido; Goldstein, Sheldon; Lukkarinen, Jani; Tumulka, Roderich
2011-01-01
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This p...
Quantum Mechanics on discrete space and time
Lorente, M
2004-01-01
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Monari, Antonio; Rivail, Jean-Louis; Assfeld, Xavier
2013-02-19
Molecular mechanics methods can efficiently compute the macroscopic properties of a large molecular system but cannot represent the electronic changes that occur during a chemical reaction or an electronic transition. Quantum mechanical methods can accurately simulate these processes, but they require considerably greater computational resources. Because electronic changes typically occur in a limited part of the system, such as the solute in a molecular solution or the substrate within the active site of enzymatic reactions, researchers can limit the quantum computation to this part of the system. Researchers take into account the influence of the surroundings by embedding this quantum computation into a calculation of the whole system described at the molecular mechanical level, a strategy known as the mixed quantum mechanics/molecular mechanics (QM/MM) approach. The accuracy of this embedding varies according to the types of interactions included, whether they are purely mechanical or classically electrostatic. This embedding can also introduce the induced polarization of the surroundings. The difficulty in QM/MM calculations comes from the splitting of the system into two parts, which requires severing the chemical bonds that link the quantum mechanical subsystem to the classical subsystem. Typically, researchers replace the quantoclassical atoms, those at the boundary between the subsystems, with a monovalent link atom. For example, researchers might add a hydrogen atom when a C-C bond is cut. This Account describes another approach, the Local Self Consistent Field (LSCF), which was developed in our laboratory. LSCF links the quantum mechanical portion of the molecule to the classical portion using a strictly localized bond orbital extracted from a small model molecule for each bond. In this scenario, the quantoclassical atom has an apparent nuclear charge of +1. To achieve correct bond lengths and force constants, we must take into account the inner shell of
Making sense of quantum mechanics
Bricmont, Jean
2016-01-01
This book explains, in simple terms, with a minimum of mathematics, why things can appear to be in two places at the same time, why correlations between simultaneous events occurring far apart cannot be explained by local mechanisms, and why, nevertheless, the quantum theory can be understood in terms of matter in motion. No need to worry, as some people do, whether a cat can be both dead and alive, whether the moon is there when nobody looks at it, or whether quantum systems need an observer to acquire definite properties. The author’s inimitable and even humorous style makes the book a pleasure to read while bringing a new clarity to many of the longstanding puzzles of quantum physics.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Star Products for Relativistic Quantum Mechanics
Henselder, P.
2007-01-01
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Bohmian Mechanics and the Quantum Revolution
Goldstein, Sheldon
1995-01-01
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena--...
Quantum mechanics of black holes.
Witten, Edward
2012-08-03
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Quantum communication between remote mechanical resonators
Felicetti, S.; Fedortchenko, S.; Rossi, R.; Ducci, S.; Favero, I.; Coudreau, T.; Milman, P.
2017-02-01
Mechanical resonators represent one of the most promising candidates to mediate the interaction between different quantum technologies, bridging the gap between efficient quantum computation and long-distance quantum communication. Here, we introduce an interferometric scheme where the interaction of a mechanical resonator with input-output quantum pulses is controlled by an independent classical drive. We design protocols for state teleportation and direct quantum state transfer, between distant mechanical resonators. The proposed device, feasible with state-of-the-art technology, can serve as a building block for the implementation of long-distance quantum networks of mechanical resonators.
Beyond relativity and quantum mechanics: space physics
Lindner, Henry H.
2011-09-01
Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Helping Students Learn Quantum Mechanics for Quantum Computing
Singh, Chandralekha
2016-01-01
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.
Supersymmetric quantum mechanics with reflections
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Post, Sarah; Vinet, Luc [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128 (QC) H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: post@crm.umontreal.ca, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-10-28
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q {yields} -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented. (paper)
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
The Hamiltonian and path integral approaches to supersymmetric quantum mechanics were reviewed. The related path integrals for the Witten Index and for stochastic processes were discussed and shown to be indications for supersymmetry breakdown. A system where in the superpotential W(x) has assymetrical values at + or - infinity was considered. Nonperturbative strategies for studying supersymmetry breakdown were described. These strategies are based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed.
Quantum biological channel modeling and capacity calculation.
Djordjevic, Ivan B
2012-12-10
Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
Quantum Biological Channel Modeling and Capacity Calculation
Directory of Open Access Journals (Sweden)
Ivan B. Djordjevic
2012-12-01
Full Text Available Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors, and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii replication errors introduced during DNA replication process, (iii transcription errors introduced during DNA to mRNA transcription, and (iv translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
Pykacz, Jarosław
2015-01-01
This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Łukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of Birkhoff-von Neumann quantum logic in the form of a special Łukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.
Karimäki, Janne Mikael
2012-01-01
An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung's hydrodynamic formulation of QM and Louis de Broglie's and David Bohm's pilot wave models. The aims of the approach are as follows: 1) to have a clear ontology for QM, 2) to describe QM in a causal way, 3) to get rid of the wave-particle dualism in pilot wave theories, 4) to provide a theoretical framework for describing creation and annihilation of particles, and 5) to provide a possible connection between particle QM and virtual particles in QFT. These goals are achieved, if the wave function is replaced by a fluid of so called virtual particles. It is also assumed that in this fluid of virtual particles exist a few real particles and that only these real particles can be directly observed. This has relevance for the measurement problem in QM and it is found that quantum probabilities arise in a very natural way from the structure of the theory. The model presented here is very similar to a recent computati...
The formalisms of quantum mechanics an introduction
David, Francois
2015-01-01
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...
Morton, Seth Michael; Jensen, Lasse
2011-10-07
A frequency-dependent quantum mechanics/molecular mechanics method for the calculation of response properties of molecules adsorbed on metal nanoparticles is presented. This discrete interaction model/quantum mechanics (DIM/QM) method represents the nanoparticle atomistically, thus accounting for the local environment of the nanoparticle surface on the optical properties of the adsorbed molecule. Using the DIM/QM method, we investigate the coupling between the absorption of a silver nanoparticle and of a substituted naphthoquinone. This system is chosen since it shows strong coupling due to a molecular absorption peak that overlaps with the plasmon excitation in the metal nanoparticle. We show that there is a strong dependence not only on the distance of the molecule from the metal nanoparticle but also on its orientation relative to the nanoparticle. We find that when the transition dipole moment of an excitation is oriented towards the nanoparticle there is a significant increase in the molecular absorption as a result of coupling to the metal nanoparticle. In contrast, we find that the molecular absorption is decreased when the transition dipole moment is oriented parallel to the metal nanoparticle. The coupling between the molecule and the metal nanoparticle is found to be surprisingly long range and important on a length scale comparable to the size of the metal nanoparticle. A simple analytical model that describes the molecule and the metal nanoparticle as two interacting point objects is found to be in excellent agreement with the full DIM/QM calculations over the entire range studied. The results presented here are important for understanding plasmon-exciton hybridization, plasmon enhanced photochemistry, and single-molecule surface-enhanced Raman scattering.
Garla, Roobee; Kaur, Narinder; Bansal, Mohinder Pal; Garg, Mohan Lal; Mohanty, Biraja Prasad
2017-03-01
Exposure to inorganic arsenic (As) is one of the major health concerns in several regions around the world. Binding of As(III) with thiols is central to the mechanisms related to its toxicity, detoxification, and therapeutic effects. Due to its high thiol content, metallothionein (MT) is presumed to play an important role in case of arsenic toxicity. Consequences of these As-thiol interactions are not yet clear due to various difficulties in the characterization of arsenic bound proteins by spectroscopic techniques. Computational modeling can be a reliable approach in predicting the molecular structures of such complexes. This paper presents the results of a systematic study on different As(III)-thiol model compounds conducted by both ab initio and DFT methods with different Gaussian type basis sets. Proficiency of these theoretical methods has been evaluated in terms of bond lengths, bond angles, free energy, partial atomic charges, computational cost, and comparison with the experimental data. It has been demonstrated that the DFT-B3LYP/6-311+G(3df) functional offers better accuracy in predicting the structure and the UV absorption spectra of As(III)-thiol complexes. The results of the present study also helps in defining the boundaries for the core of arsenic bound MT so that quantum mechanical/molecular mechanical (QM/MM) methods can be employed to predict the structural and functional aspects of the protein. Graphical Abstract Optimized structural parameters of As(3+)-thiol model compounds.
Generalized Borel transform technique in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Epele, L.N.; Fanchiotti, H.; Garcia Canal, C.A.; Marucho, M
2003-03-13
We present the Generalized Borel Transform (GBT). This new approach allows one to obtain approximate solutions of Laplace/Mellin transform valid in both, perturbative and non-perturbative regimes. We compare the results provided by the GBT for a solvable model of quantum mechanics with those provided by standard techniques, as the conventional Borel sum, or its modified versions. We found that our approach is very efficient for obtaining both the low and the high energy behavior of the model.
Quantum mechanical studies of carbon structures
Energy Technology Data Exchange (ETDEWEB)
Bartelt, Norman Charles [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Ward, Donald [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Zhou, Xiaowang [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Foster, Michael E. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Schultz, Peter A. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Wang, Bryan M. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Univ. of California, Riverside, CA (United States); McCarty, Kevin F. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2015-10-01
Carbon nanostructures, such as nanotubes and graphene, are of considerable interest due to their unique mechanical and electrical properties. The materials exhibit extremely high strength and conductivity when defects created during synthesis are minimized. Atomistic modeling is one technique for high resolution studies of defect formation and mitigation. To enable simulations of the mechanical behavior and growth mechanisms of C nanostructures, a high-fidelity analytical bond-order potential for the C is needed. To generate inputs for developing such a potential, we performed quantum mechanical calculations of various C structures.
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
QUANTUM-MECHANICAL MODELING OF SPATIAL AND BAND STRUCTURE OF Y3AL5O12 SCINTILLATION CRYSTAL
Directory of Open Access Journals (Sweden)
I. I. Vrubel
2016-05-01
Full Text Available Spatial and electronic structures of a unit cell of yttrium-aluminum garnet have been studied. Quantum-mechanical model have been presented. Semi-empirical methods PM6 and PM7 have been used for geometry optimization of the crystal unit cell. Band structure has been calculated within density functional theory with the use of PBE exchange-correlation functional. Histograms of metal-oxygen distances for equilibrium geometry have been constructed. Comparison of the used methods has been carried out and recommendation about their applicability for such problems was given. The single-particle wave functions and energies have been calculated. The bandgap was estimated. The band structure was plotted. It was shown that the method gives reliable results for spatial and band structure of Y3Al5O12 scintillation crystal. The results of this work can be used for improvement of characteristics of garnet scintillation crystals.
Negative entropy and information in quantum mechanics
Cerf, N. J.; Adami, C.
1995-01-01
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles sug...
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
The quantum mechanics of materials
Cohen, M. L.; Heine, V.; Phillips, J. C.
1982-06-01
The prediction of the properties of materials from fundamental principles, i.e., quantum mechanics, by the use of pseudopotential theory is discussed. Following a review of previous difficulties encountered in the application of quantum theory to complex aggregates of matter, and the failures of early theories to resolve differences corresponding to important phase transitions in solids, the idea first proposed by Herring concerning the energy cancellation of valence electrons and the possibility of neglecting core electron effects is examined as the basis of pseudopotential theory. The application of the electron pseudopotential, representing the scattering strength of one atomic core with respect to a single Fourier component of one valence-electron wave, to the calculation of the scattering of an electron wave in crystalline solids is examined, and the derivation of structural properties from the pseudopotentials is discussed. Recent advances in pseudopotential theory explaining the properties of surface and interface structures, and the total energy of semiconducting materials are indicated.
Quantum mechanics: Myths and facts
Nikolic, H
2006-01-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Quantum Mechanics: Myths and Facts
Nikolić, Hrvoje
2007-11-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Deformation of noncommutative quantum mechanics
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
2016-09-01
In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .
Spinning Particles in Quantum Mechanics and Quantum Field Theory
Corradini, Olindo
2015-01-01
The first part of the lectures, given by O. Corradini, covers introductory material on quantum-mechanical Feynman path integrals, which are here derived and applied to several particle models. We start considering the nonrelativistic bosonic particle, for which we compute the exact path integrals for the case of the free particle and for the harmonic oscillator, and then describe perturbation theory for an arbitrary potential. We then move to relativistic particles, both bosonic and fermionic (spinning) particles. We first investigate them from the classical view-point, studying the symmetries of their actions, then consider their canonical quantization and path integrals, and underline the role these models have in the study of space-time quantum field theories (QFT), by introducing the "worldline" path integral representation of propagators and effective actions. We also describe a special class of spinning particles that constitute a first-quantized approach to higher-spin fields. Since the fifties the qua...
Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities
Aerts, Diederik
2012-01-01
In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality, 'superposition', 'interference', 'entanglement' and 'emergence'. This aim of QMod is to put forward a theoretical framework that has the technical power of standard quantum mechanics, namely it makes explicitly use of the standard complex Hilbert space and its quantum mechanical calculus, but is also more general than standard quantum mechanics, in the sense that it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement. In this sense, QMod is a generalization of quantum mechanics, similar to how the general relativity manifold mathematical formalism is a generalization of special relativity and classical physics. We prove by means of a representation theorem that QMod can be used for any entity entailing the typical quantum effects mentioned above. Some examples of application of QMod in concept theory and macroscopic...
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Donets, E. E.; Pashnev, A.; Juan Rosales, J.; Tsulaia, M. M.
2000-02-01
The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the SUSY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum-mechanical models with one-quarter, one-half, and three-quarters of unbroken (broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM, while the one-dimensional N=4 SUSY QM, constructed earlier, admits only one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of partial SUSY breaking taking as an example a direct multidimensional generalization of the one-dimensional N=4 superconformal quantum-mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable systems and problems of quantum cosmology are briefly discussed.
Entropy, Topological Theories and Emergent Quantum Mechanics
Directory of Open Access Journals (Sweden)
D. Cabrera
2017-02-01
Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.
A mathematical theory for deterministic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, Gerard ' t [Institute for Theoretical Physics, Utrecht University (Netherlands); Spinoza Institute, Postbox 80.195, 3508 TD Utrecht (Netherlands)
2007-05-15
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
From Scalar Field Theories to Supersymmetric Quantum Mechanics
Bazeia, D
2016-01-01
In this work we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here we unveil an interesting novelty, showing that the same scalar field model may describe distinct quantum mechanical problems.
Belloni, M.; Robinett, R. W.
2014-07-01
The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems. For the ISW and the attractive DDF potentials, Eq. (4) implies, as expected, that energy eigenfunctions will have a kink-a discontinuous first derivative at the location of the infinite jump(s) in the potentials. However, the large |p| behavior of the momentum-space energy eigenfunction given by Eq. (5) will be |ϕ(p)|∝1/p2. Therefore for the ISW and the attractive DDF potentials, expectation value of p will be finite, but even powers of p higher than 2 will not lead to convergent integrals. This analysis proves that despite the kinks in the ISW and attractive DDF eigenfunctions, is finite, and therefore yield appropriate solutions to the Schrödinger equation.The existence of power-law ‘tails’ of a momentum distribution as indicated in Eq. (5) in the case of ‘less than perfect’ potentials [41], including a 1/p2 power-law dependence for a singular potential (such as the DDF form) may seem a mathematical artifact, but we note two explicit realizations of exactly this type of behavior in well-studied quantum systems.As noted below (in Section 6.2) the momentum-space energy eigenfunction of the ground state of one of the most familiar (and singular) potentials, namely that of the Coulomb problem, is given by ϕ1,0,0(p)=√{8p0/π}p0/2 where p0=ħ/a0 with a0 the Bohr radius. This prediction for the p-dependence of the hydrogen ground state momentum-space distribution was verified by Weigold [42] and collaborators with measurements taken out to p-values beyond 1.4p0; well out onto the power-law
Correspondence Truth and Quantum Mechanics
Karakostas, Vassilios
2015-01-01
The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state...
Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G
2009-07-02
We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.
Quantum localization of Classical Mechanics
Batalin, Igor A
2016-01-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum localization of classical mechanics
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Quantum dissipative Higgs model
Energy Technology Data Exchange (ETDEWEB)
Amooghorban, Ehsan, E-mail: Ehsan.amooghorban@sci.sku.ac.ir; Mahdifar, Ali, E-mail: mahdifar_a@sci.sku.ac.ir
2015-09-15
By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers–Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir’s oscillators frequencies to be nearly on resonance.
BiHermitian supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto [Dipartimento di Fisica, Universita degli Studi di Bologna, V Irnerio 46, I-40126 Bologna (Italy)
2007-04-21
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian Supersymmetric Quantum Mechanics
Zucchini, R
2006-01-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian supersymmetric quantum mechanics
Zucchini, Roberto
2007-04-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
Quantum mechanics for applied physics and engineering
Fromhold, Albert T
2011-01-01
This excellent text, directed to upper-level undergraduates and graduate students in engineering and applied physics, introduces the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics.The first three chapters introduce quantum mechanics (using the Schrödinger equations), quantum statistics, and the free-electron theory of metals. Ch
Löytynoja, T; Niskanen, J; Jänkälä, K; Vahtras, O; Rinkevicius, Z; Ågren, H
2014-11-20
Using ethanol-water solutions as illustration, we demonstrate the capability of the hybrid quantum mechanics/molecular mechanics (QM/MM) paradigm to simulate core photoelectron spectroscopy: the binding energies and the chemical shifts. An integrated approach with QM/MM binding energy calculations coupled to preceding molecular dynamics sampling is adopted to generate binding energies averaged over the solute-solvent configurations available at a particular temperature and pressure and thus allowing for a statistical assessment with confidence levels for the final binding energies. The results are analyzed in terms of the contributions in the molecular mechanics model-electrostatic, polarization, and van der Waals-with atom or bond granulation of the corresponding MM charge and polarizability force-fields. The role of extramolecular charge transfer screening of the core-hole and explicit hydrogen bonding is studied by extending the QM core to cover the first solvation shell. The results are compared to those obtained from pure electrostatic and polarizable continuum models. Particularly, the dependence of the carbon 1s binding energies with respect to the ethanol concentration is studied. Our results indicate that QM/MM can be used as an all-encompassing model to study photoelectron binding energies and chemical shifts in solvent environments.
The emerging quantum the physics behind quantum mechanics
Pena, Luis de la; Valdes-Hernandez, Andrea
2014-01-01
This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physi...
Potentiality, Actuality, and Quantum Mechanics
Directory of Open Access Journals (Sweden)
Boris Koznjak
2007-12-01
Full Text Available In this paper a possible interpretative value of Aristotle’s fundamental ontological doctrine of potentiality (δύναµις and actuality (ἐνέργεια is considered in the context of operationally undoubtedly the most successful but interpretatively still controversial theory of modern physics – quantum mechanics – especially regarding understanding the nature of the world, the phenomena of which it describes and predicts so successfully. In particular, beings of the atomic world are interpreted as real potential beings (δυνάµει ὄντα actualized by the measurement process in appropriate experimental arrangement, and the problem of actual beings (ἐνεργείᾳ ὄντα of the atomic world (better known as the measurement problem in quantum mechanics is considered in the context of Aristotle’s threefold requirement for the priority of actuality over potentiality – in time (χρόνος, definition or knowledge (λόγος, and substantiality (οὐσία.
A Quantum Mechanical Approach to Nuclear Rotations
Zettili, Nouredine
2014-09-01
We deal with the study of collective motion within the context of a quantum mechanical method - the nuclear Born-Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we utilize the NBO method to study non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. We also focus on a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described by a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states. Additionally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model. We deal with the study of collective motion within the context of a quantum mechanical method - the nuclear Born-Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we utilize the NBO method to study non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. We also focus on a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described by a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states
Bridging classical and quantum mechanics
Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.
2016-10-01
Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.
Jacquet, Philippe; Joly, Véronique
1998-01-01
Twisting the non-locality concept in quantum mechanics we introduce the hypothetical concept of retro-information. We analyse the effect of paradoxal coupling on source of retro-information in order to quantify the new means of computing that could be derived from such an hypothetical concept.
Emergent quantum mechanics and emergent symmetries
Hooft, G. 't
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such
Balázs, András
2016-01-01
The Heisenberg-James-Stapp (quantum mechanical) mind model is surveyed and criticized briefly. The criticism points out that the model, while being essentially consistent concerning (human) consciousness, fundamentally lacks the evolutional point of view both onto- and phylogenetically. Ethology and other than Jamesian psychology is quoted and a quantum mechanical theoretical scheme is suggested to essentially extend Stapp's frame in an evolutionary context. It is proposed that its central supposition, spontaneous quantum measurement can be better utilized in an investigation of the origin of the "subjective" process, having come about concomitantly with the chemistry of the origin of life. We dwell on its applicability at this latter process, at its heart standing, it is supposed, the endophysical nonlinear "self-measurement" of (quantum mechanically describable) matter, and so our investigation is extended to this primeval phenomenon. It is suggested that the life phenomenon is an indirect C* → (W*) → C* quantum algebraic process transition, where the (W*) system would represent the living state. Summarized also are our previous results on an internalized, "reversed", time process, introduced originally by Gunji, which is subordinated to the external "forwards" time evolution, driving towards symmetry by gradual space-mappings, where the original splitting-up must have come about in a spontaneous symmetry breaking nonlinear "self-measurement" of matter in an endophysical World.
Energy Technology Data Exchange (ETDEWEB)
Whitaker, A [Department of Physics, Queen' s University, Belfast (United Kingdom)
2004-02-27
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding
Schwinger Algebra for Quaternionic Quantum Mechanics
Horwitz, L P
1997-01-01
It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \\to \\infty$.
Bohmian mechanics and the quantum revolution
Goldstein, S
1995-01-01
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.
Quantum mechanics and computation; Quanta y Computacion
Energy Technology Data Exchange (ETDEWEB)
Cirac Sasturain, J. I.
2000-07-01
We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs.
Interactive learning tutorials on quantum mechanics
Singh, Chandralekha
2016-01-01
We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs) which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as a self-study tool.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Quantum Mechanics As A Limiting Case of Classical Mechanics
Ghose, Partha
2000-01-01
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which quantum mechanics emerges as a limiting case of classical mechanics in which the classical system is decoupled from its environment.
BOOK REVIEWS: Quantum Mechanics: Fundamentals
Whitaker, A.
2004-02-01
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a
Chulhai, Dhabih V; Jensen, Lasse
2015-05-28
Plasmonic circular dichroism (CD) of chiral molecules in the near field of plasmonic nanoparticles (NPs) may be used to enhance molecular CD signatures or to induce a CD signal at the plasmon resonance. A recent few-states theory explored these effects for model systems and showed an orientation dependence of the sign of the induced CD signal for spherical NPs. Here, we use the discrete interaction model/quantum mechanical (DIM/QM) method to simulate the CD and plasmonic CD of the 310- and α-helix conformations of a short alanine peptide. We find that the interactions between the molecule and the plasmon lead to significant changes in the CD spectra. In the plasmon region, we find that the sign of the CD depends strongly on the orientation of the molecule as well as specific interactions with the NP through image dipole effects. A small enhancement of the CD is found in the molecular region of the spectrum, however, the molecular signatures may be significantly altered through interactions with the NP. We also show that the image dipole effect can result in induced plasmonic CD even for achiral molecules. Overall, we find that the specific interactions with the NP can lead to large changes to the CD spectrum that complicates the interpretation of the results.
Quantum mechanics of Proca fields
Zamani, Farhad; Mostafazadeh, Ali
2009-05-01
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.
A modern approach to quantum mechanics
Townsend, John S
2012-01-01
Using an innovative approach that students find both accessible and exciting, A Modern Approach to Quantum Mechanics, Second Edition lays out the foundations of quantum mechanics through the physics of intrinsic spin. Written to serve as the primary textbook for an upper-division course in quantum mechanics, Townsend's text gives professors and students a refreshing alternative to the old style of teaching, by allowing the basic physics of spin systems to drive the introduction of concepts such as Dirac notation, operators, eigenstates and eigenvalues, time evolution in quantum mechanics, and entanglement. Chapters 6 through 10 cover the more traditional subjects in wave mechanics-the Schrodinger equation in position space, the harmonic oscillator, orbital angular momentum, and central potentials-but they are motivated by the foundations developed in the earlier chapters. Students using this text will perceive wave mechanics as an important aspect of quantum mechanics, but not necessarily the core of the subj...
Noncommutative Spacetime Symmetries from Covariant Quantum Mechanics
Directory of Open Access Journals (Sweden)
Alessandro Moia
2017-01-01
Full Text Available In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates. However, spacetime noncommutativity can also be introduced into single-particle covariant quantum mechanics, replacing the commuting operators representing the particle’s spacetime coordinates with noncommuting ones. In this paper, we provide a full characterization of a wide class of physically sensible single-particle noncommutative spacetime models and the associated deformed relativistic symmetries. In particular, we prove that they can all be obtained from the standard Minkowski model and the usual Poincaré transformations via a suitable change of variables. Contrary to previous studies, we find that spacetime noncommutativity does not affect the dispersion relation of a relativistic quantum particle, but only the transformation properties of its spacetime coordinates under translations and Lorentz transformations.
Quantum mechanics II a second course in quantum theory
Landau, Rubin H
2004-01-01
Here is a readable and intuitive quantum mechanics text that covers scattering theory, relativistic quantum mechanics, and field theory. This expanded and updated Second Edition - with five new chapters - emphasizes the concrete and calculable over the abstract and pure, and helps turn students into researchers without diminishing their sense of wonder at physics and nature.As a one-year graduate-level course, Quantum Mechanics II: A Second Course in Quantum Theory leads from quantum basics to basic field theory, and lays the foundation for research-oriented specialty courses. Used selectively, the material can be tailored to create a one-semester course in advanced topics. In either case, it addresses a broad audience of students in the physical sciences, as well as independent readers - whether advanced undergraduates or practicing scientists
Quantum Mechanics: Bell and Quantum Entropy for the Classroom
Pluch, Philipp
2014-01-01
In this article we are willing to give some first steps to quantum mechanics and a motivation of quantum mechanics and its interpretation for undergraduate students not from physics. After a short historical review in the development we discuss philosophical, physical and mathematical interpretation. We define local realism, locality and hidden variable theory which ends up in the EPR paradox, a place where questions on completeness and reality comes into play. The fundamental result of the last century was maybe Bell's that states that local realism is false if quantum mechanics is true. From this fact we can obtain the so called Bell inequalities. After a didactic example of the fact what these inequalities means we describe the key concept of quantum entanglement motivated here by quantum information theory. Also classical entropy and von Neuman entropy is discussed.
Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.
1993-01-01
We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...
Pragmatic Information in Quantum Mechanics
Roederer, Juan G
2015-01-01
An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism ...
Morlet Wavelets in Quantum Mechanics
Directory of Open Access Journals (Sweden)
John Ashmead
2012-11-01
Full Text Available Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or δ function decomposition. Morlet wavelets in particular are well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. But to take full advantage of Morlet wavelets we need to supply an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We construct both here.Quanta 2012; 1: 58–70.
Kindergarten Quantum Mechanics lectures notes
Coecke, B
2005-01-01
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.
Quantum Tunneling In Deformed Quantum Mechanics with Minimal Length
Guo, Xiaobo; Tao, Jun; Wang, Peng
2016-01-01
In the deformed quantum mechanics with a minimal length, one WKB connection formula through a turning point is derived. We then use it to calculate tunnelling rates through potential barriers under the WKB approximation. Finally, the minimal length effects on two examples of quantum tunneling in nuclear and atomic physics are discussed
A Local Interpretation of Quantum Mechanics
Lopez, Carlos
2016-04-01
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the "virtual" paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.
Lecture Script: Introduction to Computational Quantum Mechanics
Schmied, Roman
2014-01-01
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, fo...
Testing non-associative quantum mechanics
Bojowald, Martin; Buyukcam, Umut
2015-01-01
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Algebraic-statistical approach to quantum mechanics
Slavnov, D A
2001-01-01
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative algebra (observables) and the nonlinear functionals on this algebra (physical states) are used as the primary constituents. The functionals associate with results of a particular measurement. It is suggested to consider certain ensembles of the physical states as quantum states of the standart quantum mechanics. It is shown that in such scheme the mathematical formalism of the standart quantum mechanics can be reproduced completely.
Counting Trees in Supersymmetric Quantum Mechanics
Cordova, Clay
2015-01-01
We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N=2 systems. The ground state degeneracy may be written as a multi-dimensional contour integral, and the enumeration of poles can be simply phrased as counting bipartite trees. We solve this combinatorics problem, thereby obtaining exact formulas for the degeneracies of an infinite class of models. We also develop an algorithm to compute the angular momentum of the ground states, and present explicit expressions for the refined indices of theories where one rank is small.
Gawron, Piotr; Kurzyk, Dariusz; Puchała, Zbigniew
2013-05-01
We consider an extension of discrete time Markov chain queueing model to the quantum domain by use of discrete time quantum Markov chain. We introduce methods for numerical analysis of such models. Using these tools we show that quantum model behaves fundamentally different from the classical one.
Random Matrix theory approach to Quantum mechanics
Chaitanya, K. V. S. Shiv
2015-01-01
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional ...
Review of student difficulties in upper-level quantum mechanics
National Research Council Canada - National Science Library
Chandralekha Singh; Emily Marshman
2015-01-01
... at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different...
Elucidating reaction mechanisms on quantum computers.
Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias
2017-07-18
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
The transactional interpretation of quantum mechanics
Cramer, John G.
2001-06-01
The transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."
Quantum Mechanics of Palladium Nanostructures
Hira, Ajit; McKeough, James; Ortiz, Bridget; Diaz, Juan
We continue our interest in the chemisorption of different atomic and molecular species on small clusters of metallic elements, by examining the interactions of H, H2, Li and O adsorbates with Pdn clusters (n = 2 thru 20). The study of clusters can reveal the effects of substrate geometry on the behavior of adsorbates. Transition-metal clusters are especially suited for the study of quantum size effects and for formation of metallic states, and are ideal candidates for catalytic processes. Hybrid ab initio methods of quantum chemistry (particularly the DFT-B3LYP model) are used to derive optimal geometries for the clusters of interest. We compare calculated binding energies, bond-lengths, ionization potentials, electron affinities and HOMO-LUMO gaps for the clusters. Of particular interest are the comparisons of binding strengths at the three important types of sites: edge (E), hollow (H), on-top (T), threefold sites and fourfold sites. Effects of crystal symmetries corresponding to the bulk structures are investigated. The capacity of Pd clusters to adsorb H atoms will be compared to Ni clusters. Admixture with Pt atoms will also be considered.
Anisimov, Victor M; Cavasotto, Claudio N
2011-06-23
To build the foundation for accurate quantum mechanical (QM) simulation of biomacromolecules in an aqueous environment, we undertook the optimization of the COnductor-like Screening MOdel (COSMO) atomic radii and atomic surface tension coefficients for different semiempirical Hamiltonians adhering to the same computational conditions recently followed in the simulation of biomolecular systems. This optimization was achieved by reproducing experimental hydration free energies of a set consisting of 507 neutral and 99 ionic molecules. The calculated hydration free energies were significantly improved by introducing a multiple atomic-type scheme that reflects different chemical environments. The nonpolar contribution was treated according to the scaled particle Claverie-Pierotti formalism. Separate radii and surface tension coefficient sets have been developed for AM1, PM3, PM5, and RM1 semiempirical Hamiltonians, with an average unsigned error for neutral molecules of 0.64, 0.66, 0.73, and 0.71 kcal/mol, respectively. Free energy calculation of each molecule took on average 0.5 s on a single processor. The new sets of parameters will enhance the quality of semiempirical QM calculations using COSMO in biomolecular systems. Overall, these results further extend the utility of QM methods to chemical and biological systems in the condensed phase.
Critique of Conventional Relativistic Quantum Mechanics.
Fanchi, John R.
1981-01-01
Following an historical sketch of the development of relativistic quantum mechanics, a discussion of the still unresolved difficulties of the currently accepted theories is presented. This review is designed to complement and update the discussion of relativistic quantum mechanics presented in many texts used in college physics courses. (Author/SK)
On the Classical Limit of Quantum Mechanics
Allori, V; Allori, Valia; Zangh\\`{\\i}, Nino
2001-01-01
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\\h \\to 0$ asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.
Conference on Mathematical Results in Quantum Mechanics
Exner, Pavel; Tater, Miloš; QMath-7
1999-01-01
At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.
Propagators in Polymer Quantum Mechanics
Flores-González, Ernesto; Reyes, Juan D
2013-01-01
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green's function character. Furthermore they are also shown to reduce to the usual Schr\\"odinger propagators in the limit of sm...
Wang, Jimin; Askerka, Mikhail; Brudvig, Gary W; Batista, Victor S
2017-02-10
Understanding structure-function relations in photosystem II (PSII) is important for the development of biomimetic photocatalytic systems. X-ray crystallography, computational modeling, and spectroscopy have played central roles in elucidating the structure and function of PSII. Recent breakthroughs in femtosecond X-ray crystallography offer the possibility of collecting diffraction data from the X-ray free electron laser (XFEL) before radiation damage of the sample, thereby overcoming the main challenge of conventional X-ray diffraction methods. However, the interpretation of XFEL data from PSII intermediates is challenging because of the issues regarding data-processing, uncertainty on the precise positions of light oxygen atoms next to heavy metal centers, and different kinetics of the S-state transition in microcrystals compared to solution. Here, we summarize recent advances and outstanding challenges in PSII structure-function determination with emphasis on the implementation of quantum mechanics/molecular mechanics techniques combined with isomorphous difference Fourier maps, direct methods, and high-resolution spectroscopy.
Quantum Semiotics: A Sign Language for Quantum Mechanics
Prashant
2006-01-01
Semiotics is the language of signs which has been used effectively in various disciplines of human scientific endeavor. It gives a beautiful and rich structure of language to express the basic tenets of any scientific discipline. In this article we attempt to develop from first principles such an axiomatic structure of semiotics for Quantum Mechanics. This would be a further enrichment to the already existing well understood mathematical structure of Quantum Mechanics but may give new insights and understanding to the theory and may help understand more lucidly the fundamentality of Nature which Quantum Theory attempts to explain.
Directory of Open Access Journals (Sweden)
Dan Alexandru Anghel
2012-01-01
Full Text Available In semiconductor laser modeling, a good mathematical model gives near-reality results. Three methods of modeling solutions from the rate equations are presented and analyzed. A method based on the rate equations modeled in Simulink to describe quantum well lasers was presented. For different signal types like step function, saw tooth and sinus used as input, a good response of the used equations is obtained. Circuit model resulting from one of the rate equations models is presented and simulated in SPICE. Results show a good modeling behavior. Numerical simulation in MathCad gives satisfactory results for the study of the transitory and dynamic operation at small level of the injection current. The obtained numerical results show the specific limits of each model, according to theoretical analysis. Based on these results, software can be built that integrates circuit simulation and other modeling methods for quantum well lasers to have a tool that model and analysis these devices from all points of view.
Modeling quantum mechanical scattering with continuous analogue of the newton method
Directory of Open Access Journals (Sweden)
Algirdas Deveikis
2013-09-01
Full Text Available Computational modelling of potential and resonant scattering for short range and Coulomb potentials was investigated in this study. The resonant scattering problem is formulated with the short range potential composed of a spherically symmetric square well and spherically symmetric square barrier. An iteration scheme of a continuous analogue of the Newton method for continuous spectral problem with correct asymptotic in uncoupled partial waves has been developed. The nonlinear representation of the scattering problem for the normalized radial Schrödinger equation is solved numerically using the difference sweep technique. The second order accuracy scheme developed allow to find scattering phases and wave functions as well as investigate their numerical evolution. The scattering phases and wave functions dependence on the scattering problem parameters have been studied.
The Gravitational Constant as a quantum mechanical expression
Roza, Engel
2016-01-01
A quantitatively verifiable expression for the Gravitational Constant is derived in terms of quantum mechanical quantities. This derivation appears to be possible by selecting a suitable physical process in which the transformation of the equation of motion into a quantum mechanical wave equation can be obtained by Einstein's geodesic approach. The selected process is the pi-meson, modeled as the one-body equivalent of a two-body quantum mechanical oscillator in which the vibrating mass is modeled as the result of the two energy fluxes from the quark and the antiquark. The quantum mechanical formula for the Gravitational Constant appears to show a quantitatively verifiable relationship with the Higgs boson as conceived in the Standard Model.
Quantum Common Causes and Quantum Causal Models
Allen, John-Mark A.; Barrett, Jonathan; Horsman, Dominic C.; Lee, Ciarán M.; Spekkens, Robert W.
2017-07-01
Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach's principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C , then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models and provide examples of how the formalism works.
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
Dorit Aharonov; Umesh Vazirani
2012-01-01
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Bibliographic guide to the foundations of quantum mechanics and quantum information
Cabello, A
2000-01-01
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.
Prologue to super quantum mechanics something is rotten in the state of quantum mechanics
Vaguine, Victor
2012-01-01
Since its foundation more than eight decades ago, quantum mechanics has been plagued by enigmas, mysteries and paradoxes and held hostage by quantum positivism. This fact strongly suggests that something is fundamentally wrong with the quantum mechanics paradigm. The best scientific minds, such as Albert Einstein, Louis de Broglie, David Bohm, Richard Feynman and others have spent years of their professional lives attempting to find resolution to the quantum mechanics predicament, with not much success. A shift of the quantum mechanics paradigm toward a deeper physics theory is long overdue.
Probabilistic Model--Checking of Quantum Protocols
Gay, S; Papanikolaou, N; Gay, Simon; Nagarajan, Rajagopal; Papanikolaou, Nikolaos
2005-01-01
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using present-day technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of PRISM, a probabilistic model-checking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniqu...
Topological strings from quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-12-15
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P{sup 2}, local P{sup 1} x P{sup 1} and local F{sub 1}. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
Topological Strings from Quantum Mechanics
Grassi, Alba; Marino, Marcos
2014-01-01
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P2, local P1xP1 and local F1. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Phys...
Strange Bedfellows: Quantum Mechanics and Data Mining
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin [SLAC National Accelerator Laboratory, Stanford, CA (United States)
2010-02-15
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
On the tomographic picture of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ibort, A., E-mail: albertoi@math.uc3m.e [Departamento de Matematicas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganes, Madrid (Spain); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G., E-mail: marmo@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Simoni, A., E-mail: simoni@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Ventriglia, F., E-mail: ventriglia@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2010-06-07
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.
Strange Bedfellows: Quantum Mechanics and Data Mining
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin; /SLAC
2009-12-16
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Corozzi, Alessandro; Mennucci, Benedetta; Cammi, Roberto; Tomasi, Jacopo
2009-12-31
A quantum mechanical investigation on the effects of the solvent and the structure on nonlinear optical activity of a class of merocyanine compounds has been conducted. The interplay of the two effects on the first hyperpolarizability, computed at density functional theory and second-order Møller-Plesset level, has been analyzed in combination with ground state properties and geometries and excited state energies and dipoles. A critical analysis of the simplified two-level model has also been presented.
A New Interpretation to The Quantum Mechanics
Feng, Yulei
2012-01-01
In this paper, we try to give a new interpretation to the quantum mechanics from the point of view of (non-relativistic) quantum field theory. After field quantization, we obtain the Heisenberg equations for the momentum and coordinate operators of the particles excited from the (Schrodinger) field. We then give the probability concepts of quantum mechanics on the base of a statistical assemble realizing the assemble interpretation. With these, we make a series of conceptual modifications to the standard quantum mechanics, especially the quantum measurement theory; in the end, we try to solve the EPR paradox with the use of our new ideas. In addition, we also give a field theoretical description to the double-slit interference experiment, obtaining the particle number distribution, in the appendix.
A new introductory quantum mechanics curriculum
Kohnle, Antje; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2013-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of interpretive aspects of quantum mechanics and quantum information theory. This article gives an overview of the resources available at the IOP website. The core text is presented as around 80 articles co-authored by leading experts that are arranged in themes and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is part of the resource. Solutions to activities are available ...
Realism and Objectivism in Quantum Mechanics
Karakostas, Vassilios
2012-01-01
The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning t...
Quantum ballistic evolution in quantum mechanics application to quantum computers
Benioff, P
1996-01-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also pr...
Quantum Mechanics Fundamentals and Applications to Technology
Singh, Jasprit
1996-01-01
Explore the relationship between quantum mechanics and information-age applications. This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulati
A condensed course of quantum mechanics
Cejnar, Pavel
2013-01-01
This book represents a concise summary of non-relativistic quantum mechanics on the level suitable for university students of physics. It covers, perhaps even slightly exceeds, a one-year course of about 50 lectures, requiring basic knowledge of calculus, algebra, classical mechanics and a bit of motivation for the quantum adventure.The exposition is succinct, with minimal narration, but witha maximum of explicit and hierarchically structured mathematical derivations. The text covers all essential topics of university courses of quantum mechanics - from general mathematical formalism to specif
Optimization of a relativistic quantum mechanical engine
Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.
2016-08-01
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
Theoretical and quantum mechanics fundamentals for chemists
Ivanov, Stefan
2006-01-01
Provides the basics of theoretical and quantum mechanics in one place and emphasizes the continuity between themUniquely presented to be used for self-taught courses covering theoretical and quantum mechanicsEach chapter includes a detailed outline, a summary, self-assessment questions for which answers can be found in the textInvaluable for chemistry undergraduate and graduate students, chemists, other non-physical scientists, engineering students of modern techniques and technology, specialists who need a better understanding of quantum mechanics.
Philosophical foundations of interpretations of quantum mechanics
Bezlepkin, Evgeny
2016-01-01
It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist definition of the vector of state. The problem lies in the incompatibility of the philosophical foundations of interpretations, which results in the difficulty of building a unified picture of the world. To solve the problem, we identify general philosophical foundation of interpretations of quantum mechanics and built their classification. We also show that in more general theories, the part of which is quantum mechanics, it is possible to integrate (reconcile) the philosophical foundations of interpretations.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Playing Games with Quantum Mechanics
Phoenix, Simon J D
2012-01-01
We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playab...
Relativistic quantum mechanics; Mecanique quantique relativiste
Energy Technology Data Exchange (ETDEWEB)
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
On the principles of quantum mechanics
Sakai, E
2004-01-01
We propose five principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, and probability principle. We deductively establish quantum mechanics on the basis of them. Then we adopt the following four guide lines. First, we do not premise the relations between dynamical variables in classical mechanics. Second, since energy and momentum are quantitatively defined in classical mechanics, we define them in quantum mechanics so that the corresponding conservation laws are satisfied in a coupling system of a quantum particle and a classical particle. Third, we define Planck's constant as a proportionality constant between energy and frequency due to one of Einstein-de Broglie formulas. Fourth, we define mass as a proportionality constant between momentum and velocity. We have succeeded to obtain the canonical commutation relations and the Schroedinger equation for a particle in an external field in the definiti...
Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, Valeriy V
2015-01-01
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Quantum Mechanics as a Principle Theory
Bub, J
1999-01-01
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999).
Quantum mechanics as electrodynamics of curvilinear waves
2002-01-01
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory.
Quantum mechanics in simple matrix form
Jordan, Thomas F
1986-01-01
With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Containing more than 100 problems, it provides an easy way to learn part of the quantum language and to employ this new skill in solving problems.
Are All Probabilities Fundamentally Quantum Mechanical?
Pradhan, Rajat Kumar
2011-01-01
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum double slit interference experiments are discussed as illustrative prototype examples. Absence of multi-order quantum interference effects in multiple-slit experiments and the Experimental tests of complementarity in Wheeler's delayed-choice type experiments are explained using the involvement of the observer.
Babaei, Hassan; Mostafazadeh, Ali
2017-08-01
A first-quantized free photon is a complex massless vector field A =(Aμ ) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H , determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.
Avoiding Negative Probabilities in Quantum Mechanics
Nyambuya, Golden Gadzirayi
2013-01-01
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative probabilities are what led the great Paul Dirac in 1928 to the esoteric discovery of the Dirac Equation. The Dirac Equation led to one of the greatest advances in our understanding of the physical world. In this reading, we ask the seemingly senseless question, "Do negative probabilities exist in quantum mechanics?" In an effort to answer this question, we arrive at the conclusion that depending on the choice one makes of the quantum probability current, one will obtain negative probabilities. We thus propose a new quantum probability current of the Klein-Gordon theory. This quantum probability current leads directly to positive definite quantum probabilities. Because these negative probabilities are in the bare Klein-Gordon theory, intrinsically a result of negative energie...
Progress in post-quantum mechanics
Sarfatti, Jack
2017-05-01
Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantum mechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantum mechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantum mechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantum mechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.
Khrennikov, Andrei
2016-01-01
The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\\"odinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be inaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity - the quantum state ("wave function"). The correspondence PCSFT to QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and th...
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.
Quantum mechanics: Thought experiments made real
Martín, Fernando
2015-02-01
Elegant experiments performed with X-rays and a double slit formed from molecular oxygen have finally made it possible to realize and test a long-standing and famous gedanken experiment in quantum mechanics.
Supersymmetric q-deformed quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
Beyond Quantum Mechanics and General Relativity
Gregori, Andrea
2010-01-01
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Four formulations of noncommutative quantum mechanics
Gouba, Laure
2016-01-01
Four formulations of noncommutative quantum mechanics are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. The four formulations are charaterized by a deformed Heisenberg algebra but differ in mathematical and conceptual overview.
Advanced quantum mechanics materials and photons
Dick, Rainer
2016-01-01
In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of�...
Quantum mechanical streamlines. I - Square potential barrier
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
On the geometrization of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Tavernelli, Ivano, E-mail: ita@zurich.ibm.com
2016-08-15
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.
Macroscopic quantum mechanics in a classical spacetime.
Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei
2013-04-26
We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
Uncertainty in quantum mechanics: faith or fantasy?
Penrose, Roger
2011-12-13
The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.
Quantum random oracle model for quantum digital signature
Shang, Tao; Lei, Qi; Liu, Jianwei
2016-10-01
The goal of this work is to provide a general security analysis tool, namely, the quantum random oracle (QRO), for facilitating the security analysis of quantum cryptographic protocols, especially protocols based on quantum one-way function. QRO is used to model quantum one-way function and different queries to QRO are used to model quantum attacks. A typical application of quantum one-way function is the quantum digital signature, whose progress has been hampered by the slow pace of the experimental realization. Alternatively, we use the QRO model to analyze the provable security of a quantum digital signature scheme and elaborate the analysis procedure. The QRO model differs from the prior quantum-accessible random oracle in that it can output quantum states as public keys and give responses to different queries. This tool can be a test bed for the cryptanalysis of more quantum cryptographic protocols based on the quantum one-way function.
Implications of conformal symmetry in quantum mechanics
Okazaki, Tadashi
2017-09-01
In conformal quantum mechanics with the vacuum of a real scaling dimension and with a complete orthonormal set of energy eigenstates, which is preferable under the unitary evolution, the dilatation expectation value between energy eigenstates monotonically decreases along the flow from the UV to the IR. In such conformal quantum mechanics, there exist bounds on scaling dimensions of the physical states and the gauge operators.
A quantum protective mechanism in photosynthesis
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-03-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
The Free-Will Postulate in Quantum Mechanics
't Hooft, Gerardus
2007-01-01
The so-called "free will axiom" is an essential ingredient in many discussions concerning hidden variables in quantum mechanics. In this paper we argue that "free will" can be defined in different ways. The definition usually employed is clearly invalid in strictly deterministic theories. A different, more precise formulation is proposed here, defining a condition that may well be a more suitable one to impose on theoretical constructions and models. Our axiom, to be referred to as the `unconstrained initial state' condition, has consequences similar to "free will", but does not clash with determinism, and appears to lead to different conclusions concerning causality and locality in quantum mechanics. Models proposed earlier by this author fall in this category. Imposing our `unconstrained initial state' condition on a deterministic theory underlying Quantum Mechanics, appears to lead to a restricted free-will condition in the quantum system: an observer has the free will to modify the setting of a measuring ...
DEMYSTIFYING QUANTUM MECHANICS: Will there be hints from LHC?
CERN. Geneva
2007-01-01
All modern theories for particles, forces and even space-time itself, use the framework provided by quantum mechanics. The Standard Model is a quantized field theory. Even superstring theory is based on quantum mechanics. There is something odd about quantum mechanics: it brilliantly allows us to predict the outcome of experiments, yet it gives confusing statements about what really is going on inside particles and fields. Suppose we would be asking for a theory that allows us to describe what actually happens in less ambiguous terms, without destroying the magnificent successes of quantum mechanics, would this help us to answer some of the great mysteries of theoretical elementary particle physics?Organiser(s): L. Alvarez-Gaume / PH-THNote: * Tea & coffee will be served at 16:00.
Antonio Gramsci's Reflection on Quantum Mechanics
Tassani, Isabella
2006-06-01
As the first step of a wider historical reconstruction of the reception of quantum mechanics in the nineteenth-century philosophy, we are going to consider Antonio Gramsci's philosophy. He asks himself about the nature of quantum objects, if their existence depends on the act of measuring by the experimenter and if this kind of relationship can be interpreted as an argument in favour of an immaterialistic philosophy. We will remark how an idealistic interpretation of quantum mechanics found a fertile field in the Italian culture, characterized by an antiscientific attitude and at the same time needing to find in science a term of comparison.
Quantum mechanics of charged particle beam optics
Khan, Sameen Ahmed
2018-01-01
Theory of charged particle beam optics is basic to the design and working of charged particle beam devices from electron microscopes to accelerator machines. Traditionally, the optical elements of the devices are designed and operated based on classical mechanics and classical electromagnetism, and only certain specific quantum mechanical aspects are dealt with separately using quantum theory. This book provides a systematic approach to quantum theory of charged particle beam optics, particularly in the high energy cases such as accelerators or high energy electron microscopy.
Can the photosynthesis first step quantum mechanism be explained?
Sacilotti, Marco; Almeida, Euclides; Mota, Claudia C. B. O.; Nunes, Frederico Dias; Gomes, Anderson S. L.
2010-01-01
Photosynthesis first step mechanism concerns the sunlight absorption and both negative and positive charges separation. Recent and important photosynthesis literature claims that this mechanism is quantum mechanics controlled, however without presenting qualitative or quantitative scientifically based mechanism. The present accepted and old-fashioned photosynthesis mechanism model suffers from few drawbacks and an important issue is the absence of driving force for negative and positive charg...
Book Review Bohmian Mechanics and Quantum Theory
Jäger, G
1999-01-01
A review of "Bohmian Mechanics and Quantum Theory: An Appraisal" (James Cushing, Arthur Fine and Sheldon Goldstein, Eds.), an extensive collection of articles on Bohmian mechanics. In addition to broad, critical overviews of Bohmian mechanics, the reviewed collection contains extensions and hybrid versions of the theory, as are several detailed applications to practical situtations.
Quantum Models of Classical World
Directory of Open Access Journals (Sweden)
Petr Hájíček
2013-02-01
Full Text Available This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties, and the problem of quantum measurement. A considerable progress has been achieved, based on four distinct new ideas. First, objective properties are associated with states rather than with values of observables. Second, all classical properties are selected properties of certain high entropy quantum states of macroscopic systems. Third, registration of a quantum system is strongly disturbed by systems of the same type in the environment. Fourth, detectors must be distinguished from ancillas and the states of registered systems are partially dissipated and lost in the detectors. The paper has two aims: a clear explanation of all new results and a coherent and contradiction-free account of the whole quantum mechanics including all necessary changes of its current textbook version.
Quantum mechanical wavefunction: visualization at undergraduate level
Chhabra, Mahima; Das, Ritwick
2017-01-01
Quantum mechanics (QM) forms the most crucial ingredient of modern-era physical science curricula at undergraduate level. The abstract ideas involved in QM related concepts pose a challenge towards appropriate visualization as a consequence of their counter-intuitive nature and lack of experiment-assisted visualization tools. At the heart of the quantum mechanical formulation lies the concept of ‘wavefunction’, which forms the basis for understanding the behavior of physical systems. At undergraduate level, the concept of ‘wavefunction’ is introduced in an abstract framework using mathematical tools and therefore opens up an enormous scope for alternative conceptions and erroneous visualization. The present work is an attempt towards exploring the visualization models constructed by undergraduate students for appreciating the concept of ‘wavefunction’. We present a qualitative analysis of the data obtained from administering a questionnaire containing four visualization based questions on the topic of ‘wavefunction’ to a group of ten undergraduate-level students at an institute in India which excels in teaching and research of basic sciences. Based on the written responses, all ten students were interviewed in detail to unravel the exact areas of difficulty in visualization of ‘wavefunction’. The outcome of present study not only reveals the gray areas in students’ conceptualization, but also provides a plausible route to address the issues at the pedagogical level within the classroom.
Lecture Notes in Quantum Mechanics
Cohen, D
2006-01-01
These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory; Entanglement; Quantum computation; Wigner-Weyl formalism; The adiabatic picture; Berry phase; Linear response theory; Kubo formula; Modern approach to scattering theory with mesoscopic orientation; Theory of the resolvent and the Green function; Gauge and Galilei Symmetries; Motion in magnetic field; Quantum Hall effect; Quantization of the electromagnetic field; Fock space formalism.
A new interpretation of quantum mechanics
Golovko, V A
2016-01-01
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields, interaction with a measuring apparatus inclusive, in a deterministic manner without any jumps. Quantum mechanics is an approximate theory because its equations follow from the above equations upon neglecting the self-field of the electron itself. Just this leads to paradoxes, seeming contradictions and jumps in quantum mechanics. The quantum mechanical wavefunction has a dual interpretation. In some problems the square of its modulus represents a real distribution of the electronic density while in others the same square determines the probability distribution of coordinates. It is shown why, given the different interpretations of the wavefunction, it satisfies one and the same Dirac or Schr\\"odinger equation. Description of many-electron systems is also considered in the star...
Socorro, J.; Nuñez, Omar E.
2017-04-01
The multi-scalar field cosmology of the anisotropic Bianchi type-I model is used in order to construct a family of potentials that are the best suited to model the inflation phenomenon. We employ the quantum potential approach to quantum mechanics due to Bohm in order to solve the corresponding Wheeler-DeWitt equation; which in turn enables us to restrict sensibly the aforementioned family of potentials. Supersymmetric Quantum Mechanics (SUSYQM) is also employed in order to constrain the superpotential function, at the same time the tools from SUSY Quantum Mechanics are used to test the family of potentials in order to infer which is the most convenient for the inflation epoch. For completeness solutions to the wave function of the universe are also presented.
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
How to teach quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Passon, Oliver [Fachbereich Physik, University of Wuppertal, Postfach 100127, 42097 Wuppertal (Germany)
2004-11-01
In the spirit and style of John S Bell's well-known paper on How to teach special relativity it is argued that a 'Bohmian pedagogy' provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
Dynamical phase transitions in quantum mechanics
Directory of Open Access Journals (Sweden)
Rotter Ingrid
2012-02-01
Full Text Available The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points, the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model and those of highly excited nuclear states (described by random ensembles differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.
Model dynamics for quantum computing
Tabakin, Frank
2017-08-01
A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.
Nonrelativistic Quantum Mechanics with Fundamental Environment
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Godina-Nava, Juan José; Torres-Vega, Gabino; López-Riquelme, Germán Octavio; López-Sandoval, Eduardo; Samana, Arturo Rodolfo; García Velasco, Fermín; Hernández-Aguilar, Claudia; Domínguez-Pacheco, Arturo
2017-02-01
Using the conventional Haberkorn approach, it is evaluated the recombination of the radical pair (RP) singlet spin state to study theoretically the cytoprotective effect of an extremely-low-frequency electromagnetic field (ELF-EMF) on early stages of hepatic cancer chemically induced in rats. The proposal is that ELF-EMF modulates the interconversion rate of singlet and triplet spin states of the RP populations modifying the products from the metabolization of carcinogens. Previously, we found that the daily treatment with ELF-EMF 120 Hz inhibited the number and area of preneoplastic lesions in chemical carcinogenesis. The singlet spin population is evaluated diagonalizing the spin density matrix through the Lanczos method in a radical pair mechanism (RPM). Using four values of the interchange energy, we have studied the variations over the singlet population. The low magnetic field effect as a test of the influence over the enzymatic chemical reaction is evaluated calculating the quantum yield. Through a bootstrap technique the range is found for the singlet decay rate for the process. Applying the quantum measurements concept, we addressed the impact toward hepatic cells. The result contributes to improving our understanding of the chemical carcinogenesis process affected by charged particles that damage the DNA.
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONGGui－Lu; YANHai－Yang; 等
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing-the center of recent heated debate,is addressed.Concepts of the mixed state and entanglement are examined,and the data in a two-qubit liquid NMR quantum computation are analyzed.the main points in this paper are;i) Density matrix describes the "state" of an average particle in an ensemble.It does not describe the state of an individual particle in an ensemble;ii) Entanglement is a property of the wave function of a microscopic particle(such as a molecule in a liquid NMR sample),and separability of the density matrix canot be used to measure the entanglement of mixed ensemble;iii) The state evolution in bulkensemble NMR quantum computation is quantum-mechanical;iv) The coefficient before the effective pure state density matrix,ε,is a measure of the simultaneity of the molecules in an ensemble,It reflets the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system.The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangeld.We conclude that effective-pure-state NMR quantum computation is genuine,not just classical simulations.
Mischenko, I.; Chuev, M.
2016-12-01
Principal difference of magnetic nanoparticles from the bulk matter which cannot be ignored when constructing upon them combined metamaterials and modern devices is the essential influence on their behavior thermal fluctuations of the environment. These disturbances lead to specific distributions of the particles characteristics and to stochastic reorientations of their magnetic moments. On the basis of quantum-mechanical representation of the particle possessing intrinsic magnetic anisotropy and being placed onto the external magnetic field we developed general approach to describe equilibrium magnetization curves and relaxation Mössbauer spectra of magnetic nanoparticles for diagnostics of magnetic nanomaterials in the whole temperature or external field ranges. This approach has universal character and may be applied not only to the systems under thermal equilibrium, but may in principle describe macroscopic dynamical phenomena such as magnetization reversal.
Measurements and mathematical formalism of quantum mechanics
Slavnov, D. A.
2007-03-01
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
On Time. 6b: Quantum Mechanical Time
Raju, C K
2008-01-01
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.
Computations in quantum mechanics made easy
Korsch, H. J.; Rapedius, K.
2016-09-01
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.
The canonical connection in quantum mechanics
Lévai, Peter; Tsutsui, I; Levay, Peter; McMullan, David; Tsutsui, Izumi
1995-01-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.
The canonical connection in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Levay, P. [Budapesti Mueszaki Egyetem, Budapest (Hungary); Mcmullan, D.; Tsutsui, Izumi
1995-04-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry`s phase, can also be found in systems which have slow variables taking values in such a coset space. (author).
Why Quantum Mechanics is Hard to Understand
Bilodeau, D
1998-01-01
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena are favored because of their clarity. Quantum phenomena, however, do not permit them. Instead, the historical and dynamical aspects of description diverge and must be expressed in different but complementary languages. Objective historical facts are recorded in terms of objects, which necessarily have an imprecise, empirical quality. Dynamics is based on quantitative abstraction from recurring patterns. The "quantum of action" is the discontinuity between these two ways of looking at the physical world.
Emergent quantum mechanics of finances
Nastasiuk, Vadim A.
2014-06-01
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.
Fourier's Law in Quantum Mechanics
Seligman, Thomas H
2010-01-01
We derive Fourier's law for a completely coherent quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the length of the system.
Advanced quantum mechanics materials and photons
Dick, Rainer
2012-01-01
Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. The textbook can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquir...
On quantum statistical mechanics; A study guide
Majewski, W. A.
2016-01-01
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical mechanics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems, and their consequences. These include the emergence of algebraic approach and the necessity of employment of infinite dimensional structures. As an illustration, a quantization of stochastic processes, new formalism...
Quantum mechanics: why complex Hilbert space?
Cassinelli, G; Lahti, P
2017-11-13
We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
The conceptual foundations of quantum mechanics
Eisenbud, Leonard
2007-01-01
This book provides a clear and logical path to understanding what quantum mechanics is about. It will be accessible to undergraduates with minimal mathematical preparation: all that is required is an open mind, a little algebra, and a first course in undergraduate physics. Quantum mechanics is arguably the most successful physical theory. It makes predictions of incredible accuracy. It provides the structure underlying all of our electronic technology, and much of our mastery over materials. But compared with Newtonian mechanics, or even relativity, its teachings seem obscure-they have no coun
Quantum mechanics of a generalised rigid body
Gripaios, Ben
2015-01-01
We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of Type I) by methods of harmonic analysis. As examples, we consider all connected and simply-connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly-solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid.
The mathematical basis for deterministic quantum mechanics
Hooft, G. 't
2006-01-01
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint
The mathematical basis for deterministic quantum mechanics
Hooft, G. 't
2007-01-01
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is
Intrinsic resonance representation of quantum mechanics
DEFF Research Database (Denmark)
Carioli, M.; Heller, E.J.; Møller, Klaus Braagaard
1997-01-01
an optimal representation, based purely on classical mechanics. ''Hidden'' constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies...
Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics
Krause, Decio
2015-01-01
Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \\ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are \\ita{non-individuals} in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are \\ita{individuals} in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics an...
Logic and probability in quantum mechanics
1976-01-01
During the academic years 1972-1973 and 1973-1974, an intensive sem inar on the foundations of quantum mechanics met at Stanford on a regular basis. The extensive exploration of ideas in the seminar led to the org~ization of a double issue of Synthese concerned with the foundations of quantum mechanics, especially with the role of logic and probability in quantum meChanics. About half of the articles in the volume grew out of this seminar. The remaining articles have been so licited explicitly from individuals who are actively working in the foun dations of quantum mechanics. Seventeen of the twenty-one articles appeared in Volume 29 of Syn these. Four additional articles and a bibliography on -the history and philosophy of quantum mechanics have been added to the present volume. In particular, the articles by Bub, Demopoulos, and Lande, as well as the second article by Zanotti and myself, appear for the first time in the present volume. In preparing the articles for publication I am much indebted to ...
Quantum Computation Beyond the Circuit Model
Jordan, Stephen P.
2008-01-01
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a ge...
Directory of Open Access Journals (Sweden)
SUBHA SUBRAMANIAM
2013-01-01
Full Text Available In this paper modeling framework for single gate conventional planar MOSFET and double gate (DG MOSFETS are reviewed. MOS Modeling can be done by either analytical modeling or compact modeling. Single gate MOSFET technology has been the choice of mainstream digital circuits for VLSI as well as for other high frequency application in the low GHZ range. The major single gate MOS modeling methods are reviewed and compared. First generation to fifth generation MOS models like BSIM & PSP are compared. The use of multiple gates has emerged as a new technology to replace the conventional planar MOSFET when itsfeature size is scaled to the sub 22nm regime. Double Gate devices seem to be attractive alternatives as they can effectively reduce the short channel effects and yield higher current drive. DGFETS are classified as Symmetric Double Gate FETs (SDGFET and Asymmetric Double Gate FETs (ADGFET. This paper covers the fundamentals of SDGFETs and ADGFETs. Drain current models for single gate MOSFETs, SDGFETs and ADGFETs are reviewed. In the Double gate MOS era the dominating quantum mechanical effects which has to be considered in two dimensional modeling are also discussed. The comparisons of drain current models for Symmetric and Asymmetric Double gate MOSFETs are done and shown with the results like limitations of the models. A brief summary of the review work is provided. The result shows a greater demand in the field of Asymmetric Double gate modeling which can be extended for circuits like SRAM and RF amplifier design. Thepremier quantum mechanical effects which should be included in model development for below 22nm devices are listed.
Quantum mechanics and quantum information a guide through the quantum world
Fayngold, Moses
2013-01-01
Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.
Some thoughts about consciousness: from a quantum mechanics perspective.
Gargiulo, Gerald J
2013-08-01
The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning.
Quantum Mechanics as Quantum Information (and only a little more)
Fuchs, C
2002-01-01
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part--but not all--of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though taking quant-ph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory--it is the in...
Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics
Hooft, Gerard t
2012-01-01
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible mappings from the position operators q_i and their quantum canonical operators p_i of a canonical theory, onto the discrete, commuting operators Q_i and P_i. In this paper we are particularly interested in harmonic oscillators. In the discrete system, these t...
Models of optical quantum computing
Directory of Open Access Journals (Sweden)
Krovi Hari
2017-03-01
Full Text Available I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.
Quantum protocols within Spekkens' toy model
Disilvestro, Leonardo; Markham, Damian
2017-05-01
Quantum mechanics is known to provide significant improvements in information processing tasks when compared to classical models. These advantages range from computational speedups to security improvements. A key question is where these advantages come from. The toy model developed by Spekkens [R. W. Spekkens, Phys. Rev. A 75, 032110 (2007), 10.1103/PhysRevA.75.032110] mimics many of the features of quantum mechanics, such as entanglement and no cloning, regarded as being important in this regard, despite being a local hidden variable theory. In this work, we study several protocols within Spekkens' toy model where we see it can also mimic the advantages and limitations shown in the quantum case. We first provide explicit proofs for the impossibility of toy bit commitment and the existence of a toy error correction protocol and consequent k -threshold secret sharing. Then, defining a toy computational model based on the quantum one-way computer, we prove the existence of blind and verified protocols. Importantly, these two last quantum protocols are known to achieve a better-than-classical security. Our results suggest that such quantum improvements need not arise from any Bell-type nonlocality or contextuality, but rather as a consequence of steering correlations.
Multichannel framework for singular quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
Non-locality beyond quantum mechanics
Popescu, Sandu
2010-01-01
Quantum mechanics is, without any doubt, a tremendously successful theory: it started by explaining black-body radiation and the photoelectric effect, it explained the spectra of atoms, and then went on to explain chemical bonds, the structure of atoms and of the atomic nucleus, the properties of crystals and the elementary particles, and a myriad of other phenomena. Yet it is safe to say that we still lack a deep understanding of quantum mechanics – surprising and even puzzling new effects continue to be discovered with regularity. That we are surprised and puzzled is the best sign that we still don't understand; however, the veil over the mysteries of quantum mechanics is starting to lift a little.
Holism, Physical Theories and Quantum Mechanics
Seevinck, M P
2004-01-01
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. I propose an operational criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if some determination (measurement) of the global properties in the theory which can be determined by global measurements, can not be implemented by local operations and classical communication. This approach is contrasted with the well known approaches to holism in terms of supervenience. I will argue that the latter have a limited scope and need to be extended using the criterion for holism proposed here in order to satisfactory address the issue for physical theories. I formalize this criterion for classical particle physics and Bohmian mechanics as represented on a Cartesian phase and configuration space, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum ope...
Introductory quantum mechanics for applied nanotechnology
Kim, Dae Mann
2015-01-01
This introductory textbook covers fundamental quantum mechanics from an application perspective, considering optoelectronic devices, biological sensors and molecular imagers as well as solar cells and field effect transistors. The book provides a brief review of classical and statistical mechanics and electromagnetism, and then turns to the quantum treatment of atoms, molecules, and chemical bonds. Aiming at senior undergraduate and graduate students in nanotechnology related areas like physics, materials science, and engineering, the book could be used at schools that offer interdisciplinary but focused training for future workers in the semiconductor industry and for the increasing number of related nanotechnology firms, and even practicing people could use it when they need to learn related concepts. The author is Professor Dae Mann Kim from the Korea Institute for Advanced Study who has been teaching Quantum Mechanics to engineering, material science and physics students for over 25 years in USA and Asia.
Manzoni, Vinícius; Lyra, Marcelo L; Coutinho, Kaline; Canuto, Sylvio
2011-10-14
A combination of the polarizable continuum model (PCM) and the hybrid quantum mechanics/molecular mechanics (QM/MM) methodology, PCM-MM/QM, is used to include the solute electronic polarization and then study the solvent effects on the low-lying n→π(∗) excitation energy and the (15)N nuclear magnetic shielding of pyrazine and pyridazine in aqueous environment. The results obtained with PCM-MM/QM are compared with two other procedures, i.e., the conventional PCM and the iterative and sequential QM/MM (I-QM/MM). The QM calculations are made using density functional theory in the three procedures. For the excitation energies, the time-dependent B3LYP/6-311+G(d) model is used. For the magnetic shielding, the B3LYP/aug-pcS2(N)/pcS2(C,O,H) is used with the gauge-including atomic orbitals. In both cases, i.e., PCM-MM/QM and I-QM/MM, that use a discrete model of the solvent, the solute is surrounded by a first shell of explicit water molecules embedded by an electrostatic field of point charges for the outer shells. The best results are obtained including 28 explicit water molecules for the spectral calculations and 9 explicit water molecules for the magnetic shielding. Using the PCM-MM/QM methodology the results for the n→π(∗) excitation energies of pyridazine and pyrazine are 32,070 ± 80 cm(-1) and 32,675 ± 60 cm(-1), respectively, in good agreement with the corresponding I-MM/QM results of 32,540 ± 80 cm(-1) and 32,710 ± 60 cm(-1) and the experimental results of 33,450-33,580 cm(-1) and 32,700-33,300 cm(-1). For the (15)N magnetic shielding, the corresponding numbers for the gas-water shifts obtained with PCM-MM/QM are 47.4 ± 1.3 ppm for pyridazine and 19.7 ± 1.1 ppm for pyrazine, compared with the I-QM/MM values of 53.4 ± 1.3 ppm and 19.5 ± 1.2 ppm and the experimental results of 42-54 ppm and 17-22 ppm, respectively. The agreement between the two procedures is found to be very good and both are in agreement with the experimental values. PCM
Gallilei covariant quantum mechanics in electromagnetic fields
Directory of Open Access Journals (Sweden)
H. E. Wilhelm
1985-01-01
Full Text Available A formulation of the quantum mechanics of charged particles in time-dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocity w is in magnitude comparable with the velocity of light c. The electromagnetic substratum velocity w occurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.
Quantum Mechanical Studies of DNA and LNA
DEFF Research Database (Denmark)
Koch, Troels; Shim, Irene; Lindow, Morten;
2014-01-01
Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the e......Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies...
An Axiomatic Basis for Quantum Mechanics
Cassinelli, Gianni; Lahti, Pekka
2016-10-01
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
Quantum mechanics new approaches to selected topics
Lipkin, Harry J
2007-01-01
Acclaimed as ""excellent"" (Nature) and ""very original and refreshing"" (Physics Today), this collection of self-contained studies is geared toward advanced undergraduates and graduate students. Its broad selection of topics includes the Mössbauer effect, many-body quantum mechanics, scattering theory, Feynman diagrams, and relativistic quantum mechanics.Author Harry J. Lipkin, a well-known teacher at Israel's Weizmann Institute, takes an unusual approach by introducing many interesting physical problems and mathematical techniques at a much earlier point than in conventional texts. This meth
A new introductory quantum mechanics curriculum
Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2014-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.
Wilczura-Wachnik, Hanna; Jónsdóttir, Svava Osk
2003-04-01
A method for calculating interaction parameters traditionally used in phase-equilibrium computations in low-molecular systems has been extended for the prediction of solvent activities of aromatic polymer solutions (polystyrene+methylcyclohexane). Using ethylbenzene as a model compound for the repeating unit of the polymer, the intermolecular interaction energies between the solvent molecule and the polymer were simulated. The semiempirical quantum chemical method AM1, and a method for sampling relevant internal orientations for a pair of molecules developed previously were used. Interaction energies are determined for three molecular pairs, the solvent and the model molecule, two solvent molecules and two model molecules, and used to calculated UNIQUAC interaction parameters, a(ij) and a(ji). Using these parameters, the solvent activities of the polystyrene 90,000 amu+methylcyclohexane system, and the total vapor pressures of the methylcyclohexane+ethylbenzene system were calculated. The latter system was compared to experimental data, giving qualitative agreement. Figure Solvent activities for the methylcylcohexane(1)+polystyrene(2) system at 316 K. Parameters aij (blue line) obtained with the AM1 method; parameters aij (pink line) from VLE data for the ethylbenzene+methylcyclohexane system. The abscissa is the polymer weight fraction defined as y2(x1)=(1mx1)M2/[x1M1+(1mx1)M2], where x1 is the solvent mole fraction and Mi are the molecular weights of the components.
Capoferri, Luigi; Lodola, Alessio; Rivara, Silvia; Mor, Marco
2015-03-23
Irreversible epidermal growth factor receptor (EGFR) inhibitors can circumvent resistance to first-generation ATP-competitive inhibitors in the treatment of nonsmall-cell lung cancer. They covalently bind a noncatalytic cysteine (Cys797) at the surface of EGFR active site by an acrylamide warhead. Herein, we used a hybrid quantum mechanics/molecular mechanics (QM/MM) potential in combination with umbrella sampling in the path-collective variable space to investigate the mechanism of alkylation of Cys797 by the prototypical covalent inhibitor N-(4-anilinoquinazolin-6-yl) acrylamide. Calculations show that Cys797 reacts with the acrylamide group of the inhibitor through a direct addition mechanism, with Asp800 acting as a general base/general acid in distinct steps of the reaction. The obtained reaction free energy is negative (ΔA = -12 kcal/mol) consistent with the spontaneous and irreversible alkylation of Cys797 by N-(4-anilinoquinazolin-6-yl) acrylamide. Our calculations identify desolvation of Cys797 thiolate anion as a key step of the alkylation process, indicating that changes in the intrinsic reactivity of the acrylamide would have only a minor impact on the inhibitor potency.
Bueren-Calabuig, Juan A; Pierdominici-Sottile, Gustavo; Roitberg, Adrian E
2014-06-05
Chagas' disease, also known as American trypanosomiasis, is a lethal, chronic disease that currently affects more than 10 million people in Central and South America. The trans-sialidase from Trypanosoma cruzi (T. cruzi, TcTS) is a crucial enzyme for the survival of this parasite: sialic acids from the host are transferred to the cell surface glycoproteins of the trypanosome, thereby evading the host's immune system. On the other hand, the sialidase of T. rangeli (TrSA), which shares 70% sequence identity with TcTS, is a strict hydrolase and shows no trans-sialidase activity. Therefore, TcTS and TrSA represent an excellent framework to understand how different catalytic activities can be achieved with extremely similar structures. By means of combined quantum mechanics-molecular mechanics (QM/MM, SCC-DFTB/Amberff99SB) calculations and umbrella sampling simulations, we investigated the hydrolysis mechanisms of TcTS and TrSA and computed the free energy profiles of these reactions. The results, together with our previous computational investigations, are able to explain the catalytic mechanism of sialidases and describe how subtle differences in the active site make TrSA a strict hydrolase and TcTS a more efficient trans-sialidase.
Nakayama, Ryuichi
2011-01-01
A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in de Sitter spacetime seen by a static patch observer. It is found that the action integral of this model is automatically expressed by a complex integral over the time variable t along a closed contour in a way which is typical to the Schwinger-Keldysh formalism of a thermofield theory. Hence this model is at finite temperature. The case of conformally coupled scalar fields in 3d Schwarzschild de Sitter space is also considered and then a large-N matrix model is obtained.
Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics
Bauer, M
2016-01-01
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1
A multiscale quantum mechanics/electromagnetics method for device simulations.
Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua
2015-04-07
Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantum mechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantum mechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantum mechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.
Quantum Mechanics in the Light of Quantum Cosmology
Gell-Mann, Murray; Hartle, James B.
We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its
Toward an Information-based Interpretation of Quantum Mechanics and the Quantum-Classical Transition
Roederer, Juan G
2011-01-01
I will show how an objective definition of the concept of information and the consideration of recent results about information-processing in the human brain help clarify some fundamental and often counter-intuitive aspects of quantum mechanics. In particular, I will discuss entanglement, teleportation, non-interaction measurements and decoherence in the light of the fact that pragmatic information, the one our brain handles, can only be defined in the classical macroscopic domain; it does not operate in the quantum domain. This justifies viewing quantum mechanics as a discipline dealing with mathematical models and procedures aimed exclusively at predicting possible macroscopic changes and their likelihood that a given quantum system may cause when it interacts with its environment, including man-made devices such as measurement instruments. I will discuss the informational and neurobiological reasons of why counter-intuitive aspects arise whenever we attempt to construct mental images of the "inner workings...
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
The Emergent Copenhagen Interpretation of Quantum Mechanics
Hollowood, Timothy J
2013-01-01
We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint p...
Practical quantum mechanics modern tools and applications
Manousakis, Efstratios
2016-01-01
Quantum mechanics forms the foundation of all modern physics, including atomic, nuclear, and molecular physics, the physics of the elementary particles, condensed matter physics. Modern astrophysics also relies heavily on quantum mechanics. Quantum theory is needed to understand the basis for new materials, new devices, the nature of light coming from stars, the laws which govern the atomic nucleus, and the physics of biological systems. As a result the subject of this book is a required course for most physics graduate students. While there are many books on the subject, this book targets specifically graduate students and it is written with modern advances in various fields in mind. Many examples treated in the various chapters as well as the emphasis of the presentation in the book are designed from the perspective of such problems. For example, the book begins by putting the Schrodinger equation on a spatial discrete lattice and the continuum limit is also discussed, inspired by Hamiltonian lattice gauge ...
Using quantum mechanics to synthesize electronic devices
Schmidt, Petra; Levi, Anthony
2005-03-01
Adaptive quantum design [1] has been used to explore the possibility of creating new classes of electronic semiconductor devices. We show how non-equilibrium electron transmission through a synthesized conduction band potential profile can be used to obtain a desired current - voltage characteristic. We illustrate our methodology by designing a two-terminal linear resistive element in which current is limited by quantum mechanical transmission through a potential profile and power is dissipated non-locally in the electrodes. As electronic devices scale to dimensions in which the physics of operation is dominated by quantum mechanical effects, classical designs fail to deliver the desired functionality. Our device synthesis approach is a way to realize device functionality that may not otherwise be achieved. [1] Y.Chen, R.Yu, W.Li, O.Nohadani, S.Haas, A.F.J. Levi, Journal of Applied Physics, Vol.94, No.9, p6065, 2003
Quantum model for mode locking in pulsed semiconductor quantum dots
Beugeling, W.; Uhrig, Götz S.; Anders, Frithjof B.
2016-12-01
Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is dramatically increased if the system is subjected to a magnetic field and to repeated optical pulsing. This enhancement is due to mode locking: oscillation frequencies resonant with the pulsing frequencies are enhanced, while off-resonant oscillations eventually die out. Because the resonant frequencies are determined by the pulsing frequency only, the system becomes immune to frequency shifts caused by the nuclear coupling and by slight variations between individual quantum dots. The effects remain even after the optical pulsing is terminated. In this work, we explore the phenomenon of mode locking from a quantum mechanical perspective. We treat the dynamics using the central-spin model, which includes coupling to 10-20 nuclei and incoherent decay of the excited electronic state, in a perturbative framework. Using scaling arguments, we extrapolate our results to realistic system parameters. We estimate that the synchronization to the pulsing frequency needs time scales in the order of 1 s .
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; YAN Hai-Yang; LI Yan-Song; TU Chang-Cun; ZHU Sheng-Jiang; RUAN Dong; SUN Yang; TAO Jia-Xun; CHEN Hao-Ming
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing the center of recent heated debate,is addressed. Concepts of the mixed state and entanglement are examined, and the data in a two-qubit liquid NMRquantum computation are analyzed. The main points in this paper are: i) Density matrix describes the "state" of anaverage particle in an ensemble. It does not describe the state of an individual particle in an ensemble; ii) Entanglementis a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separabilityof the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The state evolution in bulk-ensemble NMRquantum computation is quantum-mechanical; iv) The coefficient before the effective pure state densitymatrix, e, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signaland has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of thedensity matrix into product states is only an indication that the ensemble can be prepared by an ensemble with theparticles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classicalsimulations.
Emerging interpretations of quantum mechanics and recent progress in quantum measurement
Clarke, M. L.
2014-01-01
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).
Riemann hypothesis and quantum mechanics
Planat, Michel; Solé, Patrick; Omar, Sami
2011-04-01
In their 1995 paper, Jean-Benoît Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β), where β is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as \\phi _{\\beta }(q)=N_{q-1}^{\\beta -1} \\psi _{\\beta -1}(N_q), where Nq = ∏qk = 1pk is the primorial number of order q and ψb is a generalized Dedekind ψ function depending on one real parameter b as \\psi _b (q)=q \\prod _{p \\in {P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}. Fix a large inverse temperature β > 2. The RH is then shown to be equivalent to the inequality N_q |\\phi _\\beta (N_q)|\\zeta (\\beta -1) \\gt e^\\gamma log log N_q, for q large enough. Under RH, extra formulas for high-temperature KMS states (1.5 < β < 2) are derived. 'Number theory is not pure Mathematics. It is the Physics of the world of Numbers.' Alf van der Poorten
A new exact quantum mechanical propagator
Wiegel, F.W.; Andel, van P.W.
1987-01-01
The authors derive a closed-form expression for the time-dependent propagator for a quantum mechanical particle which is subject to an external force which is the sum of (i) a reflecting half-plane barrier with a straight edge, and (ii) a harmonic force pointing towards a point of the edge. This new
Quantum mechanics for two-timers
Indian Academy of Sciences (India)
P Mitra
2001-02-01
Extensions of standard quantum mechanics with joint probability distributions for position coordinates and momenta have been proposed in the literature. Time is assumed to be onedimensional in these studies. In view of recent interest in two-dimensional time, the construction is extended to this situation and found to satisfy the necessary consistency conditions.
Quantum Mechanical Effects in Gravitational Collapse
Greenwood, Eric
2010-01-01
In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the pos...
Student Difficulties with Quantum Mechanics Formalism
Singh, Chandralekha
2016-01-01
We discuss student difficulties in distinguishing between the physical space and Hilbert space and difficulties related to the Time-independent Schroedinger equation and measurements in quantum mechanics. These difficulties were identified by administering written surveys and by conducting individual interviews with students.
Spin & Statistics in Nonrelativistic Quantum Mechanics, II
Kuckert, B; Kuckert, Bernd; Mund, Jens
2004-01-01
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.
Holism, physical theories and quantum mechanics
Seevinck, M. P.
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
Cunha, I E; Toppan, F
2016-01-01
In this paper we quantize superconformal $\\sigma$-models defined by worldline supermultiplets. Two types of superconformal mechanics, with and without a DFF term, are considered. Without a DFF term (Calogero potential only) the supersymmetry is unbroken. The models with a DFF term correspond to deformed (if the Calogero potential is present) or undeformed oscillators. For these (un)deformed oscillators the classical invariant superconformal algebra acts as a spectrum-generating algebra of the quantum theory. Besides the $osp(1|2)$ examples, we explicitly quantize the superconformally-invariant worldine $\\sigma$-models defined by the ${\\cal N}=4$ $(1,4,3)$ supermultiplet (with $D(2,1;\\alpha)$ invariance, for $\\alpha\
Govindarajan, T R
2016-01-01
Novel bound states are obtained for manifolds with singular potentials. These singular potentials require proper boundary conditions across boundaries. The number of bound states match nicely with what we would expect for black holes. Also they serve to model membrane mechanism for the black hole horizons in simpler contexts. The singular potentials can also mimic expanding boundaries elegantly, there by obtaining appropriately tuned radiation rates.
Reality without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics
Plotnitsky, Arkady
2015-01-01
First, the article considers the nature of quantum reality (the reality responsible for quantum phenomena) and the concept of realism (our ability to represent this reality) in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different (from quantum mechanics) theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, "the statistical Copenhagen interpretation," is non-realist, insofar as the description or even conception of the nature of quantum objects and processes is precluded. The second, by A. Khrennikov, is ultimately realist, because it assumes that the quantum-mechanical level of reality is underlain by a deeper level of reality, described, in a realist fashion, by a model based on the pre-quantum classical statistical field theory (PCSFT), the predict...
The computer-based model of quantum measurements
Sevastianov, L. A.; Zorin, A. V.
2017-07-01
Quantum theory of measurements is an extremely important part of quantum mechanics. Currently perturbations by quantum measurements of observable quantities of atomic systems are rarely taken into account in computing algorithms and calculations. In the previous studies of the authors, constructive model of quantum measurements has been developed and implemented in the form of symbolic and numerical calculations for the hydrogen-like atoms. This work describes a generalization of these results to the alkali metal atoms.
PT Symmetry in Classical and Quantum Statistical Mechanics
Meisinger, Peter N
2012-01-01
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviors than Hermitian systems, displaying sinusoidally-modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbor Ising (ANNNI) model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional QCD with heavy quarks at non-zero chemical potential can be solved by diagona...
Interactive Quantum Mechanics Quantum Experiments on the Computer
Brandt, S; Dahmen, H.D
2011-01-01
Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: • harmonic waves and wave packets, • free particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), • two-particle systems, coupled harmonic oscillators, • distinguishable and indistinguishable particles, • coherent and squeezed states in time-dependent motion, • quantized angular momentum, • spin and magnetic resonance, • hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies of quantum-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on spec...
On Quantum Mechanics on Noncommutative Quantum Phase Space
Institute of Scientific and Technical Information of China (English)
A.E.F. DjemaI; H. Smail
2004-01-01
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ =∈k ijθk and a momentum noncommutativity matrix parameter βij = ∈k ijβk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence ofa magnetic field B = q-1 β. For the other examples, additional correction terms depending onβ appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.
Quantum mechanical coherence, resonance, and mind
Energy Technology Data Exchange (ETDEWEB)
Stapp, H.P.
1995-03-26
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Global and Local Horizon Quantum Mechanics
Casadio, R; Giusti, A
2016-01-01
Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determine by spatially localised modes.
Quantum mechanics of 4-derivative theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [Universidad Autonoma de Madrid and Instituto de Fisica Teorica IFT-UAM/CSIC, Departamento de Fisica Teorica, Madrid (Spain); Strumia, Alessandro [Dipartimento di Fisica, Universita di Pisa (Italy); CERN, Theory Division, Geneva (Switzerland); INFN, Pisa (Italy)
2016-04-15
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm. (orig.)
Quantum mechanical coherence, resonance, and mind
Stapp, Henry P
1995-01-01
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Global and local horizon quantum mechanics
Casadio, Roberto; Giugno, Andrea; Giusti, Andrea
2017-02-01
Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes.
Quantum mechanics of 4-derivative theories.
Salvio, Alberto; Strumia, Alessandro
2016-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
The Classical and Quantum Mechanics of lazy baker Maps
Lakshminarayan, A
1993-01-01
We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from chaotic motion on the whole measure to chaos on a set of measure zero. Thus we have called these maps ``lazy baker maps.'' The aim of introducing these maps is to provide the simplest models of systems with a mixed phase space, in which there are both regular and chaotic motions. We find that despite the obviously contrived nature of these maps they provide a good model for the study of the quantum mechanics of such systems. We notice the effect of a classically chaotic fractal set of measure zero on the corresponding quantum maps, which leads to a transition in the spectral statistics. Some periodic orbits belonging to this fractal set are seen to scar several eigenfunctions.
Quantum Mechanics and Conceptual Change in High School Chemistry Textbooks.
Shiland, Thomas W.
1997-01-01
Examines the presentation of quantum mechanics in eight secondary chemistry texts for elements associated with a conceptual change model: (1) dissatisfaction; (2) intelligibility; (3) plausibility; and (4) fruitfulness. Reports that these elements were not present in sufficient quantities to promote conceptual change. Presents recommendations for…